Pertanyaan

Diketahui ( f ∘ g ) − 1 ( x ) = x + 7 3 x − 1 ; x  = − 7 dan f ( x ) = 2 x + 1 . Tentukan rumus fungsi g ( x ) !

Diketahui $(f \circ g)^{- 1} (x) = \frac{3 x - 1}{x + 7}; x \neq = - 7$ dan $f (x) = 2 x + 1$ . Tentukan rumus fungsi $g (x)$ !

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Klaim

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Pembahasan

Jika maka Ingat kembali bahwa , maka:

Jika $begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction end style$ maka $begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative c x plus b over denominator c x minus a end fraction end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x minus 1 over denominator x plus 7 end fraction space end cell row cell f o g left parenthesis x right parenthesis end cell equals cell fraction numerator negative 7 x minus 1 over denominator x minus 3 end fraction end cell end table end style$

Ingat kembali bahwa , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 x plus 1 end cell row cell f open parentheses g left parenthesis x right parenthesis close parentheses end cell equals cell 2 g left parenthesis x right parenthesis plus 1 end cell row cell fraction numerator negative 7 x minus 1 over denominator x minus 3 end fraction end cell equals cell 2 g left parenthesis x right parenthesis plus 1 end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell fraction numerator negative 7 x minus 1 over denominator x minus 3 end fraction minus 1 end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell fraction numerator negative 7 x minus 1 over denominator x minus 3 end fraction minus fraction numerator x minus 3 over denominator x minus 3 end fraction end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell fraction numerator negative 7 x minus 1 minus x plus 3 over denominator x minus 3 end fraction end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell fraction numerator negative 8 x plus 2 over denominator x minus 3 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator negative 4 x plus 1 over denominator x minus 3 end fraction end cell end table end style$

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