Pertanyaan

Diketahui f ( x ) = 4 x + 2 dan g ( x ) = x + 1 x − 3 , x  = − 1 . Invers dari ( g ∘ f ) ( x ) adalah...

Diketahui $f (x) = 4 x + 2 dan g (x) = \frac{x - 3}{x + 1}, x \neq = - 1$ . Invers dari $(g \circ f) (x)$ adalah...

$begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 4 x plus 1 over denominator 3 x plus 4 end fraction comma x not equal to negative 4 over 3 end style$
$begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator negative 3 x plus 4 end fraction comma x not equal to negative 4 over 3 end style$
$begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x minus 1 over denominator 4 x plus 4 end fraction comma x not equal to negative 1 end style$
$begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x plus 1 over denominator 4 minus 4 x end fraction comma x not equal to 1 end style$
$begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x plus 4 over denominator 4 x plus 4 end fraction comma x not equal to negative 1 end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Pertama tentukan fungsi Selanjutnya, invers fungsi sehingga, invers fungsi yaitu Jadi, jawaban yang tepat adalah D.

Pertama tentukan fungsi

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g open parentheses 4 x plus 2 close parentheses end cell row blank equals cell fraction numerator 4 x plus 2 minus 3 over denominator 4 x plus 2 plus 1 end fraction end cell row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x minus 1 over denominator 4 x plus 3 end fraction end cell end table end style$

Selanjutnya, invers fungsi $begin mathsize 14px style y equals fraction numerator a x plus b over denominator c x plus d end fraction rightwards arrow y to the power of negative 1 end exponent equals fraction numerator negative d x plus b over denominator c x minus a end fraction end style$

sehingga, invers fungsi yaitu

$begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator 4 x plus 3 end fraction rightwards arrow open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 3 x minus 1 over denominator 4 x minus 4 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 x plus 1 over denominator 4 minus 4 x end fraction end style$

Jadi, jawaban yang tepat adalah D.

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