Elysia.Patricia E
26 Juli 2023 11:01
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Elysia.Patricia E
26 Juli 2023 11:01
Pertanyaan
F ( x ) = x + 2 G ( x ) = x² - 3 Penyelesaian: a. Fog ( x) B. Fof ( x) C. Gog ( x) D. Gof ( x )
F ( x ) = x + 2
G ( x ) = x² - 3
Penyelesaian:
a. Fog ( x)
B. Fof ( x)
C. Gog ( x)
D. Gof ( x )
30
1
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Faizah N
Community
26 Juli 2023 11:31
<p>Diketahui :</p><p>f(x) = x+2</p><p>g(x) = x² - 3</p><p> </p><p>a. (fog)(x) = f(g(x))</p><p>(fog)(x) = f(x² - 3)</p><p>(fog)(x) = (x² - 3) + 2</p><p>(fog)(x) = x² - 3 + 2</p><p>(fog)(x) = x² - 1</p><p> </p><p>b. (fof)(x) = f(f(x))</p><p>(fof)(x) = f(x+2)</p><p>(fof)(x) = (x+2)+2</p><p>(fof)(x) = x+2+2</p><p>(fof)(x) = x+4</p><p> </p><p>c. (gog)(x) = g(g(x))</p><p>(gog)(x) = g(x² - 3)</p><p>(gog)(x) = (x² - 3)² - 3</p><p>(gog)(x) = (x<sup>4</sup> - 6x<sup>2</sup> + 9) - 3</p><p>(gog)(x) = x<sup>4</sup> - 6x<sup>2</sup> + 9 - 3</p><p>(gog)(x) = x<sup>4</sup> - 6x<sup>2</sup> + 6</p><p> </p><p>d. (gof)(x) = g(f(x))</p><p>(gof)(x) = g(x+2)</p><p>(gof)(x) = (x+2)² - 3</p><p>(gof)(x) = (x²+4x+2) - 3</p><p>(gof)(x) = x² +4x+2 - 3</p><p>(gof)(x) = x² +4x -1</p>
Diketahui :
f(x) = x+2
g(x) = x² - 3
a. (fog)(x) = f(g(x))
(fog)(x) = f(x² - 3)
(fog)(x) = (x² - 3) + 2
(fog)(x) = x² - 3 + 2
(fog)(x) = x² - 1
b. (fof)(x) = f(f(x))
(fof)(x) = f(x+2)
(fof)(x) = (x+2)+2
(fof)(x) = x+2+2
(fof)(x) = x+4
c. (gog)(x) = g(g(x))
(gog)(x) = g(x² - 3)
(gog)(x) = (x² - 3)² - 3
(gog)(x) = (x4 - 6x2 + 9) - 3
(gog)(x) = x4 - 6x2 + 9 - 3
(gog)(x) = x4 - 6x2 + 6
d. (gof)(x) = g(f(x))
(gof)(x) = g(x+2)
(gof)(x) = (x+2)² - 3
(gof)(x) = (x²+4x+2) - 3
(gof)(x) = x² +4x+2 - 3
(gof)(x) = x² +4x -1
· 3.9 (10)
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