Venty A
22 Juli 2025 08:13
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Venty A
22 Juli 2025 08:13
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Endang S
22 Juli 2025 13:18
<p><strong>1. f(x)=2x+3</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=2</strong><i><strong>x</strong></i><strong>+3 dan g(x)=x2</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>2</strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x+3+x22<i>x</i>+3+<i>x</i>2<br><strong>Domain</strong>: Semua bilangan real (RR)</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x+3−x22<i>x</i>+3−<i>x</i>2<br><strong>Domain</strong>: RR</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: (2x+3)(x2)=2x3+3x2(2<i>x</i>+3)(<i>x</i>2)=2<i>x</i>3+3<i>x</i>2<br><strong>Domain</strong>: RR</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: 2x+3x2<i>x</i>22<i>x</i>+3<br><strong>Domain</strong>: x≠0<i>x</i>=0</p><p><br><strong>2. f(x)=x</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong> dan g(x)=x2−1</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>2−1</strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: x+x2−1<i>x</i>+<i>x</i>2−1<br><strong>Domain</strong>: x≥0<i>x</i>≥0</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: x−x2+1<i>x</i>−<i>x</i>2+1<br><strong>Domain</strong>: x≥0<i>x</i>≥0</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: x(x2−1)<i>x</i>(<i>x</i>2−1)<br><strong>Domain</strong>: x≥0<i>x</i>≥0</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: xx2−1<i>x</i>2−1<i>x</i><br><strong>Domain</strong>: x≥0<i>x</i>≥0 dan x≠±1<i>x</i>=±1. Karena x≥0<i>x</i>≥0, maka x≠1<i>x</i>=1.<br><br><strong>3. f(x)=x2−9</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>2−9 dan g(x)=x−3</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>−3</strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: x2−9+x−3<i>x</i>2−9+<i>x</i>−3<br><strong>Domain</strong>: x2−9≥0<i>x</i>2−9≥0 → x≤−3<i>x</i>≤−3 atau x≥3<i>x</i>≥3</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: x2−9−x+3<i>x</i>2−9−<i>x</i>+3<br><strong>Domain</strong>: x≤−3<i>x</i>≤−3 atau x≥3<i>x</i>≥3</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: x2−9(x−3)<i>x</i>2−9(<i>x</i>−3)<br><strong>Domain</strong>: x≤−3<i>x</i>≤−3 atau x≥3<i>x</i>≥3</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: x2−9x−3<i>x</i>−3<i>x</i>2−9<br><strong>Domain</strong>: x≤−3<i>x</i>≤−3 atau x>3<i>x</i>>3 (karena x≠3<i>x</i>=3)</p><p><br><br><strong>4. f(x)=1x−1</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>−11 dan g(x)=x2x+1</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=2</strong><i><strong>x</strong></i><strong>+1</strong><i><strong>x</strong></i><strong></strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: 1x−1+x2x+1<i>x</i>−11+2<i>x</i>+1<i>x</i><br><strong>Domain</strong>: x≠1<i>x</i>=1 dan x≠−12<i>x</i>=−21</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: 1x−1−x2x+1<i>x</i>−11−2<i>x</i>+1<i>x</i><br><strong>Domain</strong>: x≠1<i>x</i>=1 dan x≠−12<i>x</i>=−21</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: 1x−1⋅x2x+1=x(x−1)(2x+1)<i>x</i>−11⋅2<i>x</i>+1<i>x</i>=(<i>x</i>−1)(2<i>x</i>+1)<i>x</i><br><strong>Domain</strong>: x≠1<i>x</i>=1 dan x≠−12<i>x</i>=−21</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: 1/(x−1)x/(2x+1)=2x+1x(x−1)<i>x</i>/(2<i>x</i>+1)1/(<i>x</i>−1)=<i>x</i>(<i>x</i>−1)2<i>x</i>+1<br><strong>Domain</strong>: x≠1<i>x</i>=1, x≠0<i>x</i>=0, dan x≠−12<i>x</i>=−21<br><br><br><strong>5. f(x)=1x</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>1 dan g(x)=2x3</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>32</strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: 1x+2x3<i>x</i>1+<i>x</i>32<br><strong>Domain</strong>: x>0<i>x</i>>0</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: 1x−2x3<i>x</i>1−<i>x</i>32<br><strong>Domain</strong>: x>0<i>x</i>>0</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: 1x⋅2x3=2x2<i>x</i>1⋅<i>x</i>32=<i>x</i>22<br><strong>Domain</strong>: x>0<i>x</i>>0</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: 1/x2/x3=x32x=x22/<i>x</i>31/<i>x</i>=2<i>x</i><i>x</i>3=2<i>x</i><br><strong>Domain</strong>: x>0<i>x</i>>0</p><p><br><br><br><br><strong>6. f(x)=x</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong> dan g(x)=x2−4</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>2−4</strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: x+x2−4<i>x</i>+<i>x</i>2−4<br><strong>Domain</strong>: x≥0<i>x</i>≥0 dan x2−4≥0<i>x</i>2−4≥0 → x≥2<i>x</i>≥2</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: x−x2−4<i>x</i>−<i>x</i>2−4<br><strong>Domain</strong>: x≥2<i>x</i>≥2</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: x⋅x2−4<i>x</i>⋅<i>x</i>2−4<br><strong>Domain</strong>: x≥2<i>x</i>≥2</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: xx2−4<i>x</i>2−4<i>x</i><br><strong>Domain</strong>: x≥2<i>x</i>≥2<br><br><br><strong>7. f(x)=2x−3</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>−32 dan g(x)=2x−6</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=2</strong><i><strong>x</strong></i><strong>−6</strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x−3+2x−6<i>x</i>−32+2<i>x</i>−6<br><strong>Domain</strong>: x≠3<i>x</i>=3</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x−3−2x+6<i>x</i>−32−2<i>x</i>+6<br><strong>Domain</strong>: x≠3<i>x</i>=3</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x−3⋅(2x−6)=4(x−3)x−3=4<i>x</i>−32⋅(2<i>x</i>−6)=<i>x</i>−34(<i>x</i>−3)=4 (untuk x≠3<i>x</i>=3)<br><strong>Domain</strong>: x≠3<i>x</i>=3</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: 2/(x−3)2x−6=2(x−3)(2x−6)=1(x−3)22<i>x</i>−62/(<i>x</i>−3)=(<i>x</i>−3)(2<i>x</i>−6)2=(<i>x</i>−3)21<br><strong>Domain</strong>: x≠3<i>x</i>=3</p><p><br><strong>8. f(x)=2x+64+2x</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=4+2</strong><i><strong>x</strong></i><strong>2</strong><i><strong>x</strong></i><strong>+6 dan g(x)=x+1</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=</strong><i><strong>x</strong></i><strong>+1</strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x+64+2x+x+14+2<i>x</i>2<i>x</i>+6+<i>x</i>+1<br><strong>Domain</strong>: x≠−2<i>x</i>=−2 dan x≥−1<i>x</i>≥−1</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x+64+2x−x+14+2<i>x</i>2<i>x</i>+6−<i>x</i>+1<br><strong>Domain</strong>: x≠−2<i>x</i>=−2 dan x≥−1<i>x</i>≥−1</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x+64+2x⋅x+14+2<i>x</i>2<i>x</i>+6⋅<i>x</i>+1<br><strong>Domain</strong>: x≠−2<i>x</i>=−2 dan x≥−1<i>x</i>≥−1</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: (2x+6)/(4+2x)x+1<i>x</i>+1(2<i>x</i>+6)/(4+2<i>x</i>)<br><strong>Domain</strong>: x≠−2<i>x</i>=−2 dan x>−1<i>x</i>>−1<br><br><br><strong>9. f(x)=2x−6</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=2</strong><i><strong>x</strong></i><strong>−6 dan g(x)=9−3x</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=9−3</strong><i><strong>x</strong></i></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x−6+9−3x=−x+32<i>x</i>−6+9−3<i>x</i>=−<i>x</i>+3<br><strong>Domain</strong>: RR</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: 2x−6−9+3x=5x−152<i>x</i>−6−9+3<i>x</i>=5<i>x</i>−15<br><strong>Domain</strong>: RR</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: (2x−6)(9−3x)(2<i>x</i>−6)(9−3<i>x</i>)<br><strong>Domain</strong>: RR</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: 2x−69−3x9−3<i>x</i>2<i>x</i>−6<br><strong>Domain</strong>: x≠3<i>x</i>=3<br><br><strong>10. f(x)=16−x2</strong><i><strong>f</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=16−</strong><i><strong>x</strong></i><strong>2 dan g(x)=4−x</strong><i><strong>g</strong></i><strong>(</strong><i><strong>x</strong></i><strong>)=4−</strong><i><strong>x</strong></i><strong></strong></p><p><strong>f+g</strong><i><strong>f</strong></i><strong>+</strong><i><strong>g</strong></i><strong>(x)</strong>: 16−x2+4−x16−<i>x</i>2+4−<i>x</i><br><strong>Domain</strong>: 16−x2≥016−<i>x</i>2≥0 dan 4−x≥04−<i>x</i>≥0 → −4≤x≤4−4≤<i>x</i>≤4 dan x≤4<i>x</i>≤4 → −4≤x≤4−4≤<i>x</i>≤4</p><p><strong>f−g</strong><i><strong>f</strong></i><strong>−</strong><i><strong>g</strong></i><strong>(x)</strong>: 16−x2−4−x16−<i>x</i>2−4−<i>x</i><br><strong>Domain</strong>: −4≤x≤4−4≤<i>x</i>≤4</p><p><strong>f⋅g</strong><i><strong>f</strong></i><strong>⋅</strong><i><strong>g</strong></i><strong>(x)</strong>: 16−x2⋅4−x16−<i>x</i>2⋅4−<i>x</i><br><strong>Domain</strong>: −4≤x≤4−4≤<i>x</i>≤4</p><p><strong>fg</strong><i><strong>gf</strong></i><strong>(x)</strong>: 16−x24−x4−<i>x</i>16−<i>x</i>2<br><strong>Domain</strong>: −4≤x<4−4≤<i>x</i><4 (karena 4−x≠04−<i>x</i>=0)</p>
1. f(x)=2x+3f(x)=2x+3 dan g(x)=x2g(x)=x2
f+gf+g(x): 2x+3+x22x+3+x2
Domain: Semua bilangan real (RR)
f−gf−g(x): 2x+3−x22x+3−x2
Domain: RR
f⋅gf⋅g(x): (2x+3)(x2)=2x3+3x2(2x+3)(x2)=2x3+3x2
Domain: RR
fggf(x): 2x+3x2x22x+3
Domain: x≠0x=0
2. f(x)=xf(x)=x dan g(x)=x2−1g(x)=x2−1
f+gf+g(x): x+x2−1x+x2−1
Domain: x≥0x≥0
f−gf−g(x): x−x2+1x−x2+1
Domain: x≥0x≥0
f⋅gf⋅g(x): x(x2−1)x(x2−1)
Domain: x≥0x≥0
fggf(x): xx2−1x2−1x
Domain: x≥0x≥0 dan x≠±1x=±1. Karena x≥0x≥0, maka x≠1x=1.
3. f(x)=x2−9f(x)=x2−9 dan g(x)=x−3g(x)=x−3
f+gf+g(x): x2−9+x−3x2−9+x−3
Domain: x2−9≥0x2−9≥0 → x≤−3x≤−3 atau x≥3x≥3
f−gf−g(x): x2−9−x+3x2−9−x+3
Domain: x≤−3x≤−3 atau x≥3x≥3
f⋅gf⋅g(x): x2−9(x−3)x2−9(x−3)
Domain: x≤−3x≤−3 atau x≥3x≥3
fggf(x): x2−9x−3x−3x2−9
Domain: x≤−3x≤−3 atau x>3x>3 (karena x≠3x=3)
4. f(x)=1x−1f(x)=x−11 dan g(x)=x2x+1g(x)=2x+1x
f+gf+g(x): 1x−1+x2x+1x−11+2x+1x
Domain: x≠1x=1 dan x≠−12x=−21
f−gf−g(x): 1x−1−x2x+1x−11−2x+1x
Domain: x≠1x=1 dan x≠−12x=−21
f⋅gf⋅g(x): 1x−1⋅x2x+1=x(x−1)(2x+1)x−11⋅2x+1x=(x−1)(2x+1)x
Domain: x≠1x=1 dan x≠−12x=−21
fggf(x): 1/(x−1)x/(2x+1)=2x+1x(x−1)x/(2x+1)1/(x−1)=x(x−1)2x+1
Domain: x≠1x=1, x≠0x=0, dan x≠−12x=−21
5. f(x)=1xf(x)=x1 dan g(x)=2x3g(x)=x32
f+gf+g(x): 1x+2x3x1+x32
Domain: x>0x>0
f−gf−g(x): 1x−2x3x1−x32
Domain: x>0x>0
f⋅gf⋅g(x): 1x⋅2x3=2x2x1⋅x32=x22
Domain: x>0x>0
fggf(x): 1/x2/x3=x32x=x22/x31/x=2xx3=2x
Domain: x>0x>0
6. f(x)=xf(x)=x dan g(x)=x2−4g(x)=x2−4
f+gf+g(x): x+x2−4x+x2−4
Domain: x≥0x≥0 dan x2−4≥0x2−4≥0 → x≥2x≥2
f−gf−g(x): x−x2−4x−x2−4
Domain: x≥2x≥2
f⋅gf⋅g(x): x⋅x2−4x⋅x2−4
Domain: x≥2x≥2
fggf(x): xx2−4x2−4x
Domain: x≥2x≥2
7. f(x)=2x−3f(x)=x−32 dan g(x)=2x−6g(x)=2x−6
f+gf+g(x): 2x−3+2x−6x−32+2x−6
Domain: x≠3x=3
f−gf−g(x): 2x−3−2x+6x−32−2x+6
Domain: x≠3x=3
f⋅gf⋅g(x): 2x−3⋅(2x−6)=4(x−3)x−3=4x−32⋅(2x−6)=x−34(x−3)=4 (untuk x≠3x=3)
Domain: x≠3x=3
fggf(x): 2/(x−3)2x−6=2(x−3)(2x−6)=1(x−3)22x−62/(x−3)=(x−3)(2x−6)2=(x−3)21
Domain: x≠3x=3
8. f(x)=2x+64+2xf(x)=4+2x2x+6 dan g(x)=x+1g(x)=x+1
f+gf+g(x): 2x+64+2x+x+14+2x2x+6+x+1
Domain: x≠−2x=−2 dan x≥−1x≥−1
f−gf−g(x): 2x+64+2x−x+14+2x2x+6−x+1
Domain: x≠−2x=−2 dan x≥−1x≥−1
f⋅gf⋅g(x): 2x+64+2x⋅x+14+2x2x+6⋅x+1
Domain: x≠−2x=−2 dan x≥−1x≥−1
fggf(x): (2x+6)/(4+2x)x+1x+1(2x+6)/(4+2x)
Domain: x≠−2x=−2 dan x>−1x>−1
9. f(x)=2x−6f(x)=2x−6 dan g(x)=9−3xg(x)=9−3x
f+gf+g(x): 2x−6+9−3x=−x+32x−6+9−3x=−x+3
Domain: RR
f−gf−g(x): 2x−6−9+3x=5x−152x−6−9+3x=5x−15
Domain: RR
f⋅gf⋅g(x): (2x−6)(9−3x)(2x−6)(9−3x)
Domain: RR
fggf(x): 2x−69−3x9−3x2x−6
Domain: x≠3x=3
10. f(x)=16−x2f(x)=16−x2 dan g(x)=4−xg(x)=4−x
f+gf+g(x): 16−x2+4−x16−x2+4−x
Domain: 16−x2≥016−x2≥0 dan 4−x≥04−x≥0 → −4≤x≤4−4≤x≤4 dan x≤4x≤4 → −4≤x≤4−4≤x≤4
f−gf−g(x): 16−x2−4−x16−x2−4−x
Domain: −4≤x≤4−4≤x≤4
f⋅gf⋅g(x): 16−x2⋅4−x16−x2⋅4−x
Domain: −4≤x≤4−4≤x≤4
fggf(x): 16−x24−x4−x16−x2
Domain: −4≤x<4−4≤x<4 (karena 4−x≠04−x=0)
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