Pertanyaan

Jika f ∘ g ( x ) = 4 x + 7 , g ( x ) = 2 x − 1 , tentukan rumus fungsi f ( x )

Jika $f \circ g (x) = 4 x + 7$ , $g (x) = 2 x - 1$ , tentukan rumus fungsi $f (x)$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

rumus fungsi .

rumus fungsi

Pembahasan

Diketahui dan . Perhatikan bahwa Misalkan . Maka Sehingga Jadi, rumus fungsi .

Diketahui dan .

Perhatikan bahwa

Misalkan .

Maka

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

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 x minus 1 right parenthesis end cell equals cell 4 x plus 7 space end cell row cell f left parenthesis a right parenthesis end cell equals cell 4. fraction numerator a plus 1 over denominator 2 end fraction plus 7 space end cell row cell f left parenthesis a right parenthesis end cell equals cell 2 left parenthesis a plus 1 right parenthesis plus 7 end cell row cell f left parenthesis a right parenthesis end cell equals cell 2 a plus 2 plus 7 space end cell row cell f left parenthesis a right parenthesis end cell equals cell 2 a plus 9 space end cell row cell f left parenthesis x right parenthesis end cell equals cell 2 x plus 9 end cell end table end style$

Jadi, rumus fungsi .