Question

Dadas as funçoes F(X)=3x-1eg(X)=x²+2, Calcule:

A-) (GoF)(X)
B-) (FoG)(X)
C-) (FoF)(X)
D-) (GoG)(X)

Answer 1

a)
f(x) = 3x - 1
g(x) = x² + 2

g o f ( x ) = f dentro do g

g(x) = x² + 2
g[(f (x)] = (3x - 1)² + 2 = 9x² - 2.1.3x + 1 + 2 = 9x² - 6x + 3
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b)
f(x) = 3x - 1
g(x) = x² + 2

f[g(x)] = g dentro do f

f [g(x)] = 3(x² + 2) - 1 = 3x² + 6 - 1 = 3x² + 5
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c)
f(x) = 3x - 1
(f o f) (x) = f dentro do f

f[f(x)] = 3(3x - 1) - 1 = 9x - 3 - 1 = 9x - 4
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d)

g(x) = x² + 2

g [g(x)] = (x² + 2)² + 2 = x⁴ + 2.2x² + 4 + 2 = x⁴ + 4x² + 6