diketahui f(x)=16x+30,g(x)=x-3,h(x)=2x+4,tentukan(hogof)-1(x)

f(x)=f(-1)= -1x16+30
=14
g(x)= g(-1)= -1x1-3
=-4
h(x)= h(-1)= -1x2+4
=2
Pelajaran kelas 10 ya....

Mapel : Matematika
Materi : Fungsi dan Invers Fungsi

f(x) = 16x + 30
g(x) = x - 3
h(x) = 2x + 4

(h o g o f)(x) = h(g o f)(x)

(g o f) (x) = (16x + 30) - 3
(g o f) (x) = 16x + 27

(h o g o f) (x) = 2(16x + 27) + 4
(h o g o f) (x) = 32x + 54 + 4
(h o g o f) (x) = 32x + 58

Rumus Invers Fungsi :

[tex]\boxed{f(x) = ax + b \to f^{-1}(x)= \frac{x-b}{a}}\\ \\ \\ \text{(h o g o f) (x) = 32x+58}\\a=32; b=58\\ \\ \text{(h o g o f)}^{-1} \text{(x)} = \frac{x-58}{32}\\ \\ \text{(h o g o f)}^{-1} \text{(x)}= \frac{x}{32}- \frac{58}{32}\\ \\ \text{(h o g o f)}^{-1} \text{(x)}= \frac{x}{32}- \frac{29}{16}\\ \\ \text{(h o g o f)}^{-1} \text{(x)}= \frac{x}{32}- 1\frac{13}{16} [/tex]

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