Diketahui f(x)=2x+41 dan g(x)=3x−31. Nilai (f∘g)(0)+(f∘g)−1(0)=....

Pertanyaan

Diketahui $\style{font-size:14px}f\style{font-size:14px}(\style{font-size:14px}x\style{font-size:14px})\style{font-size:14px}=\style{font-size:14px}2\style{font-size:14px}x\style{font-size:14px}+\frac{\style{font-size:14px}1}{\style{font-size:14px}4}$ dan $\style{font-size:14px}g\style{font-size:14px}(\style{font-size:14px}x\style{font-size:14px})\style{font-size:14px}=\style{font-size:14px}3\style{font-size:14px}x\style{font-size:14px}-\frac{\style{font-size:14px}1}{\style{font-size:14px}3}$ . Nilai $\style{font-size:14px}{(f\circ g)(0)+\left(f\circ g\right)^{-1}(0)=}$ ....

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui dan .

kita tentukan terlebih dahulu fungsi komposisinya:

begin mathsize 14px style equals f open parentheses 3 x minus 1 third close parentheses equals 2 open parentheses 3 x minus 1 third close parentheses plus 1 fourth equals 6 x minus 2 over 3 plus 1 fourth equals 6 x minus 5 over 12 end style

kemudian kita cari inversnya:

$size 14px y size 14px equals size 14px 6 size 14px x size 14px minus size 14px 5 over size 14px 12 size 14px 12 size 14px y size 14px equals size 14px 72 size 14px x size 14px minus size 14px 5 size 14px 12 size 14px y size 14px plus size 14px 5 size 14px equals size 14px 72 size 14px x fraction numerator size 14px 12 size 14px y size 14px plus size 14px 5 over denominator size 14px 72 end fraction size 14px equals size 14px x size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px 12 size 14px x size 14px plus size 14px 5 over denominator size 14px 72 end fraction size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px 0 size 14px right parenthesis size 14px equals fraction numerator size 14px 0 size 14px plus size 14px 5 over denominator size 14px 72 end fraction size 14px equals size 14px 5 over size 14px 72$

Nilai $begin mathsize 14px style negative 5 over 12 plus 5 over 72 equals fraction numerator negative 30 plus 5 over denominator 72 end fraction equals fraction numerator negative 25 over denominator 72 end fraction end style$

jadi, jawabannya E