Pertanyaan

Diketahui f ( x ) = 2 x − 5 , g − 1 ( x ) = 4 x + 3 dan h − 1 ( x ) = 8 x + 1 . Nilai ( f ∘ ( g ∘ h ) ) − 1 ( − 7 ) adalah....

Diketahui $f (x) = 2 x - 5, g^{- 1} (x) = \frac{x + 3}{4}$ dan $h^{- 1} (x) = 8 x + 1$ . Nilai $(f \circ (g \circ h))^{- 1} (- 7)$ adalah....

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

hasil dari .

hasil dari

Pembahasan

Dengan menggunakan konsep invers fungsi komposisi maka Tentukan dahulu . Misalkan . Sehingga didapat Dengan demikian hasil dari .

Dengan menggunakan konsep invers fungsi komposisi maka

Tentukan dahulu . Misalkan .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals y row cell 2 x minus 5 end cell equals y row cell 2 x end cell equals cell y plus 5 end cell row x equals cell fraction numerator y plus 5 over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 5 over denominator 2 end fraction end cell end table end style$

Sehingga didapat

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell h to the power of negative 1 end exponent left parenthesis x right parenthesis ring operator g to the power of negative 1 end exponent left parenthesis x right parenthesis ring operator f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell row blank equals cell h to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses f to the power of negative 1 end exponent open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses left parenthesis g to the power of negative 1 end exponent open parentheses fraction numerator x plus 5 over denominator 2 end fraction close parentheses right parenthesis close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses left parenthesis fraction numerator fraction numerator x plus 5 over denominator 2 end fraction plus 3 over denominator 4 end fraction right parenthesis close parentheses end cell row blank equals cell h to the power of negative 1 end exponent left parenthesis fraction numerator x plus 11 over denominator 8 end fraction right parenthesis end cell row blank equals cell 8 left parenthesis fraction numerator x plus 11 over denominator 8 end fraction right parenthesis plus 1 end cell row blank equals cell x plus 11 plus 1 end cell row blank equals cell x plus 12 end cell row cell left parenthesis f ring operator left parenthesis g ring operator h right parenthesis right parenthesis to the power of negative 1 end exponent left parenthesis negative 7 right parenthesis end cell equals cell negative 7 plus 12 end cell row blank equals 5 end table end style$

Dengan demikian hasil dari .