Question

Dadas as funções f(x) = x+3 e g(x) = x² - 2, determine:
a) f(g(x))
b) g(f(x))
c) f(f(x))
d) g(g(x))

Answer 1

                 $f(g(x)) = f(x^2-2) \\ f(g(x)) =(x^2+2)+3=x^2+2+3=x^2+5 \\ \\ g(f(x)) = g(x+3) \\ g(f(x))=(x+3)^2-2=x^2+6x+9-2=x^2+6x+7$

           $f(f(x))=f(x+3) \\ x(f(x))=(x+3)+3=x+3+3=x+6 \\ \\ g(g(x))=g(x^2-2) \\ g(g(x))=(x^2-2)^2-2=x^4-4x^2+2$