Let $$h(x) = f(g(x)).$$ Note that $f(x)$ and $g(x)$ are not necessarily polynomials. State for each of the following cases whether $h(x)$ is even, odd, or neither.
a) $f(x)$ and $g(x)$ are both even.
b) $f(x)$ and $g(x)$ are both odd.
c) $f(x)$ is even and $g(x)$ is odd.
d) $f(x)$ is odd and $g(x)$ is even.
+349 a) If both f and g are even, then \(h(x)=f(g(x))=f(g(-x))=h(-x)\). EVEN
b) If both f and g are odd, then \(h(-x)=f(g(-x))=f(-g(x))=-f(g(x))=-(h(x))\). ODD
c) If f is even and g is odd, then \(h(-x)=f(g(-x))=f(-g(x))=f(g(x))=h(x)\). EVEN
d) If f is odd and g is even, then \(h(x)=f(g(x))=f(g(-x))=h(-x)\). EVEN
