Question

dadas as funções f(x)=5x-8 ,g(x)=x²+4x e h(x)=2/x-3, determine:

a) f(g(x))

b) h(g(x))

c) f(h(x))

d) h(f(x))

e) g(f(x))

f) f(f(x))

g) g(g(x))

h) h(h(x))​

Answer 1

Resposta:

Explicação passo-a-passo:

a) f(g(x)) = f(x² + 4x) = 5(x² + 4x) - 8 = 5x² + 20x - 8

b) h(g(x)) = h(x² + 4x) = 2/(x² + 4x) - 3 = 2/x² + 4x - 3

c) f(h(x)) = f(2/x-3) = 5.(2/x-3)-8 = 10/x-3 -8 = (10-8x+24)/x-3 = (34-8x)/x-3

d) h(f(x)) = h(5x-8) = 2/(5x-8-3) = 2/(5x-11)

e) g(f(x)) = g(5x-8) = (5x-8)²+4x = 25x²-80x+64+4x = 25x²-76x+64

f) f(f(x)) = f(5x-8) = 5(5x-8)-8 = 25x-40-8 = 25x-48

g) g(g(x)) = g(x²+4x) = (x²+4x)²+4(x²+4x) = x⁴+8x³+16x²+4x²+16x = x⁴+8x³+20x²+16x

h) h(h(x)) = h(2/x-3) = 2/[(2/x-3)-3] = 2/[2-3x+9/x-3] = 2/[11-3x/x-3] = 2(x-3)/11-3x = 2x-6/11-3x