Pertanyaan

Diketahui fungsi f ( x ) = 2 x − 1 ,dan ( g ∘ f ) ( x ) = 2 x − 3 . Tentukan: b. ( g ∘ f ) − 1 ( x )

Diketahui fungsi $f (x) = 2 x - 1$ , dan $(g \circ f) (x) = 2 x - 3$ .
Tentukan:

b. $(g \circ f)^{- 1} (x)$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

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$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px left parenthesis size 14px g size 14px ring operator size 14px f size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator size 14px x size 14px plus size 14px 3 over denominator size 14px 2 end fraction end cell end table$ .

Pembahasan

Misalkan Jadi, .

Misalkan begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals y end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals y row cell 2 x minus 3 end cell equals y row cell 2 x end cell equals cell y plus 3 end cell row x equals cell fraction numerator y plus 3 over denominator 2 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y plus 3 over denominator 2 end fraction end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 3 over denominator 2 end fraction end cell end table end style$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px left parenthesis size 14px g size 14px ring operator size 14px f size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator size 14px x size 14px plus size 14px 3 over denominator size 14px 2 end fraction end cell end table$ .