Diketahui f(x)=2x+3, g(x)=3x−1, dan (h∘g∘f)(x)=x+4x2−1. Tentukan nilai h(0).

Pertanyaan

Diketahui $f(x)=2x+3$ , $g(x)=3x-1$ , dan $left parenthesis h ring operator g ring operator f right parenthesis left parenthesis x right parenthesis equals fraction numerator x squared minus 1 over denominator x plus 4 end fraction.$ Tentukan nilai $h(0).$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

didapat nilai dari $h(0)=\frac{28}{96}=\frac7{24}$

Pembahasan

Ingat bahwa $(h\circ g\circ f)(x)=h(g(f(x)))$ . Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis h ring operator g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell row cell h left parenthesis g left parenthesis f left parenthesis x right parenthesis right parenthesis right parenthesis end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell row cell h left parenthesis g left parenthesis 2 x plus 3 right parenthesis end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell row cell h left parenthesis 3 left parenthesis 2 x plus 3 right parenthesis minus 1 right parenthesis end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell row cell h left parenthesis 6 x plus 9 minus 1 right parenthesis end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell row cell h left parenthesis 6 x plus 8 right parenthesis end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell end table$

Misalkan: $6x+8=y$ maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell 6 x end cell equals cell y minus 8 end cell row x equals cell fraction numerator y minus 8 over denominator 6 end fraction end cell end table$

Jadi,

$table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis 6 x plus 8 right parenthesis end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell row cell h left parenthesis y right parenthesis end cell equals cell fraction numerator open parentheses begin display style fraction numerator y minus 8 over denominator 6 end fraction end style close parentheses squared minus 1 over denominator open parentheses begin display style fraction numerator y minus 8 over denominator 6 end fraction end style close parentheses plus 4 end fraction end cell row blank equals cell fraction numerator open parentheses begin display style fraction numerator y squared minus 16 y plus 64 over denominator 36 end fraction end style close parentheses minus 1 over denominator open parentheses begin display style fraction numerator y minus 8 over denominator 6 end fraction end style close parentheses plus 4 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator y squared minus 16 y plus 64 over denominator 36 end fraction end style minus begin display style 36 over 36 end style over denominator begin display style fraction numerator y minus 8 over denominator 6 end fraction end style plus begin display style 24 over 6 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator y squared minus 16 y plus 28 over denominator 36 end fraction end style over denominator begin display style fraction numerator y plus 16 over denominator 6 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator y squared minus 16 y plus 28 over denominator 36 end fraction end style over denominator begin display style fraction numerator 6 left parenthesis y plus 16 right parenthesis over denominator 36 end fraction end style end fraction end cell row cell h left parenthesis y right parenthesis end cell equals cell fraction numerator y squared minus 16 y plus 28 over denominator 6 left parenthesis y plus 16 right parenthesis end fraction end cell row cell h left parenthesis x right parenthesis end cell equals cell fraction numerator x squared minus 16 x plus 28 over denominator 6 left parenthesis x plus 16 right parenthesis end fraction end cell end table$

Sehingga nilai dari $h(0)$ adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell fraction numerator x squared minus 16 x plus 28 over denominator 6 left parenthesis x plus 16 right parenthesis end fraction end cell row cell h left parenthesis 0 right parenthesis end cell equals cell fraction numerator left parenthesis 0 right parenthesis squared minus 16 left parenthesis 0 right parenthesis plus 28 over denominator 6 left parenthesis 0 plus 16 right parenthesis end fraction end cell row blank equals cell fraction numerator 0 minus 0 plus 28 over denominator 6 left parenthesis 16 right parenthesis end fraction end cell row blank equals cell 28 over 96 end cell end table$

Dengan demikian, didapat nilai dari $h(0)=\frac{28}{96}=\frac7{24}$

1.0 (1 rating)

Pertanyaan serupa

Misalkan f(x)=1−x2, g(x)=3x dan h(x)=2−x. Nilai (f∘g∘h)(1)=. . .

4.8

Jawaban terverifikasi

Diketahui fungsi f: R→R, g: R→R, dan h: R→R dengan f(x)=x+2, g(x)=3x−1, dan h(x)=x2−1. Tentukan: a. (h∘f∘g)(x)

139

4.7

Jawaban terverifikasi

Kerjakan soal dibawah ini! Fungsi f : R→R, g : R→R dan h : R→R adalah fungsi-fungsi yang ditentukan oleh f(x)=2+x, g(x)=x2−1 dan h(x)=2x. Tentukan nilai (h∘g∘f)(x) !

5.0

Jawaban terverifikasi

Diketahui fungsi f(x)=x+2, g(x)=3x−1, dan h(x)=x2−1. Tentukan : a. (h∘f∘g)(x)

0.0

Jawaban terverifikasi

Diketahui fungsi sebagai berikut: f(x)h(x)g(x)m(x)====2x+1x−4x2−3x+22x−5x+4 Tentukan: e. (m∘f∘g)(x)

0.0

Jawaban terverifikasi