Pertanyaan

Diketahui f ( x ) = 2 x + 4 1 dan g ( x ) = 3 x − 3 1 . Nilai ( f ∘ g ) ( 0 ) + ( f ∘ g ) − 1 ( 0 ) = ....

Diketahui $f (x) = 2 x + \frac{1}{4}$ dan $g (x) = 3 x - \frac{1}{3}$ . Nilai $(f \circ g) (0) + (f \circ g)^{- 1} (0) =$ ....

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui dan . kita tentukan terlebih dahulu fungsi komposisinya: kemudian kita cari inversnya: Nilai jadi, jawabannya E

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