Question

Sabendo que f(x) = 2x - 6 e g(x) = 5x + a. Determine “a” de modo que f(g(x)) = g(f(x)). *

8 pontos

a) a = - 30

b) a = - 40

c) a = - 34

d) a = - 24

e) a = - 20

alguém? ​

Answer 1

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$\sf{f[g(x)]=2g(x)-6}\\\sf{f[g(x)]=2\cdot(5x+a)=10x+2a}\\\sf{g[f(x)]=5f(x)+a=5\cdot(2x-6)+a=10x-30+a}\\\sf{f[g(x)]=g[f(x)]}\\\sf{\diagdown\!\!\!\!\!10x+2a=\diagdown\!\!\!\!\! 10x-30+a}\\\sf{2a-a=-30}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{a=-30}}}}}$