Pertanyaan

Diketahui f : R → R dan g : R → R didefinisikan dengan f ( x ) = x − 5 3 x + 1 , x  = 5 dan g ( x ) = x - 3. lnvers dari ( f o g )( x ) adalah ....

Diketahui f : R → R dan g : R → R didefinisikan dengan $f (x) = \frac{3 x + 1}{x - 5}, x \neq = 5$ dan g(x) = x - 3. lnvers dari (f o g)(x) adalah ....

$begin mathsize 14px style left parenthesis f o g right parenthesis to the power of negative 1 space end exponent left parenthesis x right parenthesis equals fraction numerator negative 8 x plus 8 over denominator x minus 3 end fraction comma space x not equal to 3 end style$
$begin mathsize 14px style left parenthesis f o g right parenthesis to the power of negative 1 space end exponent left parenthesis x right parenthesis equals fraction numerator negative 3 x plus 8 over denominator x plus 8 end fraction comma space x not equal to negative 8 end style$
$begin mathsize 14px style left parenthesis f o g right parenthesis to the power of negative 1 space end exponent left parenthesis x right parenthesis equals fraction numerator 3 x minus 8 over denominator x minus 8 end fraction comma space x not equal to 8 end style$
$begin mathsize 14px style left parenthesis f o g right parenthesis to the power of negative 1 space end exponent left parenthesis x right parenthesis equals fraction numerator 8 x minus 8 over denominator x minus 3 end fraction comma space x not equal to 3 end style$
$begin mathsize 14px style left parenthesis f o g right parenthesis to the power of negative 1 space end exponent left parenthesis x right parenthesis equals fraction numerator 8 x plus 8 over denominator x plus 3 end fraction comma space x not equal to negative 3 end style$

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$begin mathsize 14px style left parenthesis fog right parenthesis left parenthesis straight x right parenthesis equals straight f left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis space space space space space space space space space space space space space equals straight f left parenthesis straight x minus 3 right parenthesis space space space space space space space space space space space space space equals fraction numerator 3 open parentheses straight x minus 3 close parentheses plus 1 over denominator straight x minus 3 minus 5 end fraction space space space space space space space space space space space space space equals fraction numerator 3 straight x minus 8 over denominator straight x minus 8 end fraction Untuk space straight f open parentheses straight x close parentheses equals fraction numerator ax plus straight b over denominator cx plus straight d end fraction space maka space inversnya colon straight f to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator negative dx plus straight b over denominator cx minus straight a end fraction Jadi comma space invers space dari space left parenthesis fog right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 3 straight x minus 8 over denominator straight x minus 8 end fraction space adalah open parentheses fog close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 8 straight x minus 8 over denominator straight x minus 3 end fraction dengan space syarat colon space straight x minus 3 not equal to 0 space straight x not equal to 3 end style$