Answer
(a) $ e^4$
(b) $ \frac{3}{e^2}-2$
(c) $ e^{e^4}$
(d) $ -17$
Work Step by Step
Given $f(x)=e^x$ and $g(x)=3x-2$, we have
(a) $(f\circ g)(2)=f(g(2))=f(3(2)-2)=f(4)=e^4$
(b) $(g\circ f)(-2)=g(f(-2))=g(e^{-2})=3(e^{-2})-2=\frac{3}{e^2}-2$
(c) $(f\circ f)(4)=f(f(4))=f(e^4)=e^{e^4}$
(d) $(g\circ g)(-1)=g(g(-1))=g(3(-1)-2)=g(-5)=3(-5)-2=-17$
