Given f(x)= square root (x+4) and g(x)=x^2
a)g(f(5)) b)f(g(4)) c)g(f(4))
Please show steps. Thanks.
(a) $\displaystyle f(5) = 3 \Rightarrow g(f(5)) = g(3) = 9$
(b) $\displaystyle g(4) = 16 \Rightarrow f(g(4)) = \sqrt{20}$
(c) $\displaystyle f(4) = \sqrt 8 \Rightarrow g(f(4)) = 8$
OR
Observe that $\displaystyle f(g(x)) = f(x^2) = \sqrt{x^2 + 4}$
and that, $\displaystyle g(f(x)) = g(\sqrt{x+4}) = x+4$