Jika f(x)=2x−4 dan g(x)=3x+9 , tentukan: c. (f∘g)−1(x)

Pertanyaan

Jika $\style{font-size:14px}{f\left(x\right)=2x-4}$ dan $\style{font-size:14px}{g\left(x\right)=3x+9}$ , tentukan:

c. $\style{font-size:14px}{{(f\circ g)}^{-1}(x)}$

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 4 end style$

$begin mathsize 14px style g open parentheses x close parentheses equals 3 x plus 9 end style$

Ditanyakan:

$begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style$ adalah...

jawab:

pertama kita menentukan fungsi komposisi:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f open parentheses 3 x plus 9 close parentheses end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 2 left parenthesis 3 x plus 9 right parenthesis minus 4 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 6 x plus 18 minus 4 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 6 x plus 14 end cell end table end style$

Kemudian kita tentukan fungsi invers dari fungsi komposisi tersebut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 6 x plus 14 y equals 6 x plus 14 6 x equals y minus 14 x equals fraction numerator y minus 14 over denominator 6 end fraction end cell row blank blank cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 14 over denominator 6 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x minus 14 over denominator 6 end fraction end cell end table end style$

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Nasrullah

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 05 Oktober 2021