Pertanyaan

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

Diketahui fungsi $f (x) = 4 x + 2$ , dan $(g \circ f) (x) = 8 x + 3$ .
Tentukan:

Invers fungsi $g$
Nilai dari $g^{- 1} (7)$

A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

dan nilai .

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 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 x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style

dan nilai

g to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals 4

Pembahasan

a. Menentukan Misalkan: Dari definisi diperoleh: Subtitusikan permisalan di atas. b. Menentukan nilai dari . Menentukan invers terlebih dahulu. Dengan demikian, dan nilai .

a. Menentukan begin mathsize 14px style g open parentheses x close parentheses. end style

Misalkan:

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

Dari definisi begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses comma end style diperoleh:

Subtitusikan permisalan di atas.

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

b. Menentukan nilai dari begin mathsize 14px style g to the power of negative 1 end exponent open parentheses 7 close parentheses end style .

Menentukan invers terlebih dahulu.

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

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

Dengan demikian, dan nilai g to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals 4 .