Jika f(x) = x−2 dan g(x)=x+2, fungsi {(f∘g)(x)}⋅{(g∘f(x))}=....

Pertanyaan

Jika f(x) = $\style{font-size:14px}{x-2}$ dan $\style{font-size:14px}{g\left(x\right)=x+2}$ , fungsi $\left\{\left(f\circ g\right)\left(x\right)\right\}\cdot\left\{\left(g\circ f\left(x\right)\right)\right\}=....$

$begin mathsize 14px style x squared plus 4 end style$
$begin mathsize 14px style x squared minus 4 end style$
$x squared$
x + 4
$begin mathsize 14px style x minus 4 end style$

Pembahasan Video:

Pembahasan Soal:

Jika f(x) = dan , fungsi

kita cari komposisi fungsinya dulu,

$begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis equals f left parenthesis x plus 2 right parenthesis equals left parenthesis x plus 2 right parenthesis minus 2 equals x left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals g left parenthesis f left parenthesis x right parenthesis right parenthesis equals g left parenthesis x minus 2 right parenthesis equals left parenthesis x minus 2 right parenthesis plus 2 equals x left curly bracket left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis right curly bracket times left curly bracket left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis right curly bracket equals x times x equals x squared end style$

jadi, jawabannya C

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Dijawab oleh:

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Terakhir diupdate 05 Oktober 2021

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Diketahui f(x)=x2+4x+4 dan g(x)=x2−4x+4. Rumus f(g(x))+g(f(x))=....

Pembahasan Soal:

Diketahui dan . Rumus

kita sederhanakan dulu fungsinya,

= $begin mathsize 14px style open parentheses x plus 2 close parentheses squared end style$

= $begin mathsize 14px style open parentheses x minus 2 close parentheses squared end style$

kemudian tentukan dulu fungsi komposisinya:

$size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 4 plus 2 right parenthesis end style to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis end style to the power of size 14px 2 size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px g size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared plus 4 x plus 4 minus 2 right parenthesis end style to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space square root of size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px plus square root of size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px equals square root of begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis squared end style end root size 14px plus square root of size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 end root size 14px equals size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 size 14px plus size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px equals size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px 8$

jadi, jawabannya C

Roboguru

Jika f(x)=x1+x dan g(x)=x−x1, maka (g∘f)(1)=…

Pembahasan Soal:

Jika $begin mathsize 14px style f open parentheses x close parentheses equals 1 over x plus x end style$ dan $begin mathsize 14px style g open parentheses x close parentheses equals x minus 1 over x end style$ , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses 1 close parentheses end cell equals cell g open parentheses f open parentheses 1 close parentheses close parentheses end cell row blank equals cell g open parentheses 1 over 1 plus 1 close parentheses end cell row blank equals cell g open parentheses 2 close parentheses end cell row blank equals cell 2 minus 1 half end cell row blank equals cell 3 over 2 end cell end table end style$

Jadi, nilai dari $begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses 1 close parentheses end style$ adalah $begin mathsize 14px style 3 over 2 end style$ .

Roboguru

Diketahui . Jumlah semua nilai a yang memenuhi adalah ....

Pembahasan Soal:

Perhatikan bahwa

$open parentheses g ring operator f close parentheses open parentheses x close parentheses equals g open parentheses f open parentheses x close parentheses close parentheses equals g open parentheses x close parentheses$

Kemudian, diperoleh perhitungan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses a close parentheses end cell equals cell g open parentheses a close parentheses end cell row 4 equals cell 2 a squared minus 4 a plus 4 end cell row 0 equals cell 2 a squared minus 4 a plus 4 minus 4 end cell row 0 equals cell 2 a squared minus 4 a end cell row 0 equals cell 2 a open parentheses a minus 2 close parentheses end cell row cell 2 a end cell equals cell 0 blank atau blank a minus 2 equals 0 end cell row a equals cell 0 blank atau blank a equals 2 end cell end table$

Oleh karena itu, jumlah semua nilai $a$ yang memenuhi adalah $0 plus 2 equals 2$ .

Jadi, jawaban yang tepat adalah D.

Roboguru

Diketahui fungsi f:R→R dengan f(x)=x2−4x+2 dan fungsi g:R→R dengan g(x)=3x−7. Tentukanlah a) c)

Pembahasan Soal:

a) Subtitusikan $f open parentheses x close parentheses$ pada $g open parentheses x close parentheses$ .

$table attributes columnalign right center left columnspacing 0px end attributes row cell g ring operator f open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses x squared minus 4 x plus 2 close parentheses end cell row blank equals cell 3 open parentheses x squared minus 4 x plus 2 close parentheses minus 7 end cell row blank equals cell 3 x squared minus 12 x plus 6 minus 7 end cell row blank equals cell 3 x squared minus 12 x minus 1 end cell end table$

c) Maka, nilai $open parentheses g ring operator f close parentheses open parentheses 5 close parentheses$

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses 5 close parentheses end cell equals cell 3 x squared minus 12 x minus 1 end cell row blank equals cell 3 open parentheses 5 close parentheses squared minus 12 open parentheses 5 close parentheses minus 1 end cell row blank equals cell 75 minus 60 minus 1 end cell row blank equals 14 end table$

Jadi, diperoleh $Error converting from MathML to accessible text.$ dan $open parentheses g ring operator f close parentheses open parentheses 5 close parentheses equals 14$ .

Roboguru

Diketahui fungsi f(x)=3x−1 dan g(x)=2x2+4x−10. Nilai dari komposisi fungsi (g∘f)(−2) adalah ....

Pembahasan Soal:

Jika diberikan fungsi $f open parentheses x close parentheses space dan space g open parentheses x close parentheses$ maka dapat ditentukan fungsi komposisi dan nilai dari fungsi komposisi tersebut sebagai berikut.

Diketahui:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 3 x minus 1 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x squared plus 4 x minus 10 end cell end table$

Sehingga dapat ditentukan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell 2 times open parentheses f open parentheses x close parentheses close parentheses squared plus 4 times f open parentheses x close parentheses minus 10 end cell row blank equals cell 2 times open parentheses 3 x minus 1 close parentheses squared plus 4 times open parentheses 3 x minus 1 close parentheses minus 10 end cell row blank equals cell 2 times open parentheses 9 x squared minus 6 x plus 1 close parentheses plus 12 x minus 4 minus 10 end cell row blank equals cell 18 x squared minus 12 x plus 2 plus 12 x minus 4 minus 10 end cell row blank equals cell 18 x squared minus 12 end cell row cell open parentheses g ring operator f close parentheses open parentheses negative 2 close parentheses end cell equals cell g open parentheses f open parentheses negative 2 close parentheses close parentheses end cell row blank equals cell 18 times open parentheses negative 2 close parentheses squared minus 12 end cell row blank equals cell 18 times 4 minus 12 end cell row blank equals cell 72 minus 12 end cell row blank equals 60 end table$

Dengan demikian, diperoleh $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g ring operator f close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 60 end table$ .

Roboguru