Question

Jika f(x) = 5 - 4x³ dan (f o g)(x) = 4x³ + 8x² + 24x - 55, nilai g(-2) = ...

Answer 1

Penjelasan dengan langkah-langkah:

FungSee

f(x) = 5 - 4x³

f(g(x) = 4x³ + 8x² + 24x - 55

Nilai g(-2) = .....

f(g(x) = 4x³ + 8x² + 24x - 55

= f(g(x)

= 5 - 4(g(x)³

= -4(g(x)³ + 5

= (4x³ + 8x² + 24x -55 - 5) + 5

= (4x³- 8x² - 24x -60) + 5

= -4(-x³ -2x² -6x + 15) + 5

g(x)³ = (-x³-2x²-6x+15)

g(x) = ³√(-x³-2x²-6x+15)

g(-2) = ³√(-(-2)³-2(-2)²-6(-2)+15)

g(-2) = ³√(8-8+12+15)

g(-2) = ³√27)

g(-2) = 3

Answer 2

Verified answer

PEMBAHASAN

Invers Fungsi

f(x) = 5 - 4x³

f^-1 (5 - 4x³) = x

(fog)(x) = 4x³ + 8x² + 24x - 55

f^-1 (4x³ + 8x² + 24x - 55) = g(x)

g(-2) = f^-1 (4(-2)³ + 8(-2)² + 24(-2) - 55)

g(-2) = f^-1 (-103)

g(-2) = f^-1 (5 - 4x³) = x

g(-2) = f^-1 (5 - 108) = x

g(-2) = f^-1 (5 - 4.3³) = 3

g(-2) = 3