Pertanyaan

Diketahui g ( x ) = 2 x + 1 x − 1 , x  = − 2 1 . Invers fungsi g ( x ) adalah g − 1 ( x ) = ....

$Diketahui g (x) = \frac{x - 1}{2 x + 1}, x \neq = - \frac{1}{2} . Invers fungsi g (x) adalah g^{- 1} (x) = ....$

$fraction numerator 2 x plus 1 over denominator x minus 1 end fraction comma space x not equal to 1$
$fraction numerator x plus 1 over denominator 1 minus 2 x end fraction comma space x not equal to 1 half$
$fraction numerator x minus 2 over denominator 1 minus x end fraction comma space x not equal to 1$
$fraction numerator 1 minus 2 x over denominator x plus 1 end fraction comma space x not equal to negative 1$
$fraction numerator 2 x minus 1 over denominator x plus 1 end fraction comma space x not equal to negative 1$

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Klaim

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$g left parenthesis x right parenthesis space equals space fraction numerator a x plus b over denominator c x plus d end fraction comma space x not equal to negative d over c space rightwards double arrow space g to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space fraction numerator negative d x plus b over denominator c x minus a end fraction comma space x not equal to a over c Jadi comma space g left parenthesis x right parenthesis equals fraction numerator x minus 1 over denominator 2 x plus 1 end fraction space rightwards double arrow space g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative x minus 1 over denominator 2 x minus 1 end fraction equals fraction numerator x plus 1 over denominator 1 minus 2 x end fraction comma space x not equal to 1 half$