Question

PLS Bantu mo dikumpul...

jika f(x) = x+2, g(x) = x^3-1 dan h(x) = 2x
Tentukanlah (h o g o f)^-1 dan (h o g o f)^-1 (2)

Answer 1

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

(h o g o f)(x) = h(g(x + 2))

(h o g o f)(x) = h((x + 2)³ - 1)

(h o g o f)(x) = h((x + 2)³ - 1)

(h o g o f)(x) = 2((x + 2)³ - 1)

(h o g o f)(x) = 2(x + 2)³ - 2

(h o g o f)^-1(x) = ³√((x + 2)/2) - 2

(h o g o f)^-1(2) = ³√((2 + 2)/2) - 2

(h o g o f)^-1(2) = ³√(4/2) - 2

(h o g o f)^-1(2) = ³√2 - 2