Pertanyaan

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

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

Tentukan:

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

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Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Pembahasan

Diketahui fungsi . Menentukan Misalkan , sehingga a. Jadi, . Menentukan b. Jadi, .

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

Menentukan

Misalkan begin mathsize 14px style a equals x minus 2 space maka space x equals a plus 2 end style , sehingga

a. Jadi, begin mathsize 14px style g left parenthesis x right parenthesis equals 2 x plus 1 end style .

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

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

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