(a) Given a function
\[ \begin{align}
h(x) &= \sqrt{\frac{x^2-1}{x^2-3}}
\end{align} \ \]
rewrite h(x) as the composition of two functions f(x) and g(x) in two different ways.
(b) given two functions f(x) and g(x), when does the domain of f(g(x)) have the same domain as g(x)?
Suppose
\[ \begin{align}
f(x) &= x+1 \quad \text{and} \\
g(x) &= x^2
\end{align} \ \]
(a) Find a formula for
\[ \begin{align}
f(g(x))
\end{align} \ \]
(b) Find a formula for
\[ \begin{align}
g(f(x))
\end{align} \ \]
(a) Explain why an even function is not 1 to 1.
(b) Given
\[ \begin{align}
f(x) &= x^3 + x
\end{align} \ \]
Evaluate f-1(x) for four different values of x.
Is it possible to find a formula for f-1(x)?