Question

dadas as funções f(x)= -5x+2 e g(x)= -x-1, determine:

f(f(x))=

g(g(x))=

f(g(x))=

g(f(x))=

f(g(f(-1))=

g(f(g(2))=

Answer 1

Explicação passo-a-passo:

f(f(x)) = -5(-5x + 2) + 2

f(f(x)) = 25x - 10 + 2

f(f(x)) = 25x - 8

g(g(x)) = -(-x - 1) - 1

g(g(x)) = x + 1 - 1

g(g(x)) = x

f(g(x)) =  -5(-x - 1) + 2

f(g(x)) =  5x + 5 + 2

f(g(x)) = 5x + 7

g(f(x)) = -(-5x + 2) - 1

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

g(f(x)) = 5x - 3

f(g(f(-1)) = -5(-(-5(-1) + 2) - 1) + 2

f(g(f(-1)) = -5(-(5 + 2) - 1) + 2

f(g(f(-1)) = -5(-(7 - 1)) + 2

f(g(f(-1)) = -5(-6) + 2

f(g(f(-1)) = 30 + 2

f(g(f(-1)) = 32

g(f(g(2)) = -(-5(-2 - 1) + 2) - 1

g(f(g(2)) = -(-5(-3) + 2) - 1

g(f(g(2)) = -(15 + 2) - 1

g(f(g(2)) = -17 - 1

g(f(g(2)) = -18