If \( f(x) = x^2 \) and \( g(x) = 2^x \)
(a) Find \( g(f(2)) \)
(b) What is the range of \( g(f(x)) \) ?
(c) Show \( g(-x) = 1/g(x) \).
Solve
If
\[ \begin{align}
f(x) &= \frac{1}{\sqrt x} \quad \text{and} \quad g(x)= x^2-1
\end{align}\ \]
(a) Find f(g(x))
(b) Find g(f(x))
(c) What is the domain of f(g(x))?
Solve
Find the inverse function of \[ \begin{align} y &= \frac{1}{x-1} \quad \end{align}\ \] for x > 0, y > 0 and sketch its graph.
Solve
Find the inverse function of \[ \begin{align} y &= \sqrt x \\ \end{align}\ \] for x > 0, y > 0 and sketch its graph.
Solve