Diketahui fungsi f(x)=4x+2 dan (g∘f)(x)=8x+3. Tentukan: a. Invers fungsi g b. Nilai dari g−1(7)

Pertanyaan

Diketahui fungsi $\style{font-size:14px}{f(x)=4x+2\;\mathrm{dan}\;(g\circ f)(x)=8x+3}$ .

Tentukan:

a. Invers fungsi $\style{font-size:14px}g$

b. Nilai dari $\style{font-size:14px}{g^{-1}(7)}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals 4 end style

Pembahasan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x plus 2 space dan space left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals 8 x plus 3 end style .

Menentukan begin mathsize 14px style g left parenthesis x right parenthesis end style .

Misalkan begin mathsize 14px style a equals 4 x plus 2 space end style maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a minus 2 end cell equals cell 4 x end cell row cell fraction numerator a minus 2 over denominator 4 end fraction end cell equals x end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis a right parenthesis end cell equals cell 8 left parenthesis fraction numerator a minus 2 over denominator 4 end fraction right parenthesis plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 left parenthesis a minus 2 right parenthesis plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 a minus 4 plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 a minus 1 end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 1 end cell end table end style$

Menentukan invers fungsi begin mathsize 14px style g end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 1 end cell row y equals cell 2 x minus 1 end cell row cell y plus 1 end cell equals cell 2 x end cell row cell fraction numerator y plus 1 over denominator 2 end fraction end cell equals x row cell fraction numerator y plus 1 over denominator 2 end fraction end cell equals cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell row cell fraction numerator x plus 1 over denominator 2 end fraction end cell equals cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table end style$

a. Jadi, $begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator 2 end fraction end style$ .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent left parenthesis 7 right parenthesis end cell equals cell fraction numerator 7 plus 1 over denominator 2 end fraction end cell row blank equals cell 8 over 2 end cell row blank equals 4 end table end style$

b. Jadi, nilai dari begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals 4 end style .