Pertanyaan

Diketahui f ( x ) = 5 x + 7 dan g ( x ) = 3 x + 4 2 x − 6 , x  = 3 − 4 , Tentukan ( g ∘ f ) − 1 ( x ) !

Diketahui $f (x) = 5 x + 7$ dan $g (x) = \frac{2 x - 6}{3 x + 4}, x \neq = \frac{- 4}{3}$ , Tentukan $(g \circ f)^{- 1} (x)$ !

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

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$left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 8 minus 25 y over denominator 15 y minus 10 end fraction$ .

Pembahasan

Dengan menggunakan konsep komposisi fungsi diperoleh: Jadi, .

Dengan menggunakan konsep komposisi fungsi diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell Misalkan space left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals y row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell fraction numerator 2 left parenthesis 5 x plus 7 right parenthesis minus 6 over denominator 3 left parenthesis 5 x plus 7 right parenthesis plus 4 end fraction end cell row blank equals cell fraction numerator 10 x plus 8 over denominator 15 x plus 25 end fraction end cell row y equals cell fraction numerator 10 x plus 8 over denominator 15 x plus 25 end fraction end cell row cell y left parenthesis 15 x plus 25 right parenthesis end cell equals cell 10 x plus 8 end cell row cell 15 x y plus 25 y end cell equals cell 10 x plus 8 end cell row cell 15 x y minus 10 x end cell equals cell 8 minus 25 y end cell row cell x left parenthesis 15 y minus 10 right parenthesis end cell equals cell 8 minus 25 y end cell row x equals cell fraction numerator 8 minus 25 y over denominator 15 y minus 10 end fraction end cell end table$

Jadi, $left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 8 minus 25 y over denominator 15 y minus 10 end fraction$ .