Jika f(x)=x−1xdan g(x)=x+1, nilai (f∘g)−1(2)=....

Pertanyaan

Jika $size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px x over denominator size 14px x size 14px minus size 14px 1 end fraction$ dan $\style{font-size:14px}g\style{font-size:14px}(\style{font-size:14px}x\style{font-size:14px})\style{font-size:14px}=\style{font-size:14px}x\style{font-size:14px}+\style{font-size:14px}1$ , nilai $\style{font-size:14px}{{(f\circ g)}^{-1}(2)=}$ ....

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

maka kita tentukan dahulu fungsi komposisinya :

$begin mathsize 14px style equals f left parenthesis x plus 1 right parenthesis equals fraction numerator left parenthesis x plus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis minus 1 end fraction equals fraction numerator x plus 1 over denominator x end fraction end style$

kemudian kita cari inversnya :

$begin mathsize 14px style y equals fraction numerator x plus 1 over denominator x end fraction x y equals x plus 1 x y minus x equals 1 x left parenthesis y minus 1 right parenthesis equals 1 x equals fraction numerator 1 over denominator y minus 1 end fraction open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 1 over denominator x minus 1 end fraction open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis 2 right parenthesis equals fraction numerator 1 over denominator 2 minus 1 end fraction equals 1 over 1 equals 1 end style$

jadi, jawabannya D