Question

Dadas as funções f(x) = x+3 e g(x) = 2x-3 determine
a) f(g(x))
b) g(f(x))
c) f(f(x))
d)g(g(x))

Answer 1

$f(x)=x+3 \\ g(x)=2x-3 \\ a) f(g(x))= 2.g(x)+3 \\ f(g(x))=2.(2x-3)+3 = 4x-6+3=4x-3 \\ b) g(f(x))=2.(f(x))-3=2(x+3)-3 \\ g(f(x))=2x+6-3=2x+3 \\ c)f(f(x))=f(x)+3=x+3+3=x+6 \\ d) g(g(x))=2.(g(x))-3=2(2x-3)-3=4x-6-3=4x-9$