Pertanyaan

Tentukan ( f ∘ g ) − 1 ( x ) dan ( g ∘ f ) − 1 ( x ) jika diketahui f ( x ) = 3 − x 1 dan g ( x ) = x + 4 !

Tentukan $(f \circ g)^{- 1} (x) dan (g \circ f)^{- 1} (x)$ jika diketahui $f (x) = \frac{1}{3 - x} dan g (x) = x + 4$ !

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan menggunakan konsepinvers fungsi komposisi: Sehingga, Selanjutnya, Sehingga, Jadi,

Dengan menggunakan konsep invers fungsi komposisi:

Sehingga,

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

Selanjutnya,

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 13 minus 4 x over denominator 3 minus x end fraction end cell row y equals cell fraction numerator 13 minus 4 x over denominator 3 minus x end fraction end cell row cell 3 y minus y x end cell equals cell 13 minus 4 x end cell row cell y x plus 4 x end cell equals cell 13 minus 3 y end cell row cell x left parenthesis y plus 4 right parenthesis end cell equals cell 13 minus 3 y end cell row x equals cell fraction numerator 13 minus 3 y over denominator y plus 4 end fraction end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 13 minus 3 x over denominator x plus 4 end fraction end cell end table$

Jadi,

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

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 13 minus 3 x over denominator x plus 4 end fraction end cell end table$