Pertanyaan

Diketahui fungsi f ( x ) = 2 x + 5 dan g ( x ) = x − 6 3 x + 2 , x  = 6 . Jika invers fungsi f ( x ) = f − 1 ( x ) dan invers fungsi g ( x ) = g − 1 ( x ) . Tentukan: a . f − 1 ( x ) b . g − 1 ( x )

Diketahui fungsi $f (x) = 2 x + 5 dan g (x) = \frac{3 x + 2}{x - 6}, x \neq = 6$ .

Jika invers fungsi $f (x) = f^{- 1} (x)$ dan invers fungsi $g (x) = g^{- 1} (x)$ .

Tentukan:

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

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Jawaban terverifikasi

Jawaban

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 x plus 2 over denominator x minus 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table end style$

Pembahasan

Diketahui Menentukan a. Jadi, . Menentukan b. Jadi,

Diketahui $begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 5 space dan space g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 6 end fraction comma x not equal to 6 end style$

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

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 x plus 5 end cell row y equals cell 2 x plus 5 end cell row cell y minus 5 end cell equals cell 2 x end cell row cell fraction numerator y minus 5 over denominator 2 end fraction end cell equals x row cell fraction numerator y minus 5 over denominator 2 end fraction end cell equals cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell row cell fraction numerator x minus 5 over denominator 2 end fraction end cell equals cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell row blank blank blank end table end style$

a. Jadi, $begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 5 over denominator 2 end fraction end style$ .

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

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x plus 2 over denominator x minus 6 end fraction end cell row y equals cell fraction numerator 3 x plus 2 over denominator x minus 6 end fraction end cell row cell y left parenthesis x minus 6 right parenthesis end cell equals cell 3 x plus 2 end cell row cell x y minus 6 y end cell equals cell 3 x plus 2 end cell row cell x y minus 3 x end cell equals cell 6 y plus 2 end cell row cell x left parenthesis y minus 3 right parenthesis end cell equals cell 6 y plus 2 end cell row x equals cell fraction numerator 6 y plus 2 over denominator y minus 3 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 6 y plus 2 over denominator y minus 3 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 6 x plus 2 over denominator x minus 3 end fraction comma space x not equal to 3 end cell row blank blank blank row blank blank blank end table end style$

b. Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 x plus 2 over denominator x minus 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table end style$

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