Practice questions on how to find the inverse of a function are presented below. Each question has a detailed solution available on a separate page.
Find the inverse of the linear function \( f \).
\[ f(x) = 3x - 2 \]
Find the inverse of the quadratic function \( f \).
\[ f(x) = -x^2 + 2, \quad x \ge 0 \]
Find the inverse of the quadratic function \( f \).
\[ f(x) = x^2 - 2x, \quad x \ge 1 \]
Find the inverse of the rational function \( f \).
\[ f(x) = \frac{2}{x} \]
Find the inverse of the rational function \( f \).
\[ f(x) = \frac{x + 1}{x - 1} \]
Find the inverse of the square root function \( f \).
\[ f(x) = \sqrt{x - 1} \]
Find the inverse of the cube root function \( f \).
\[ f(x) = (x + 1)^{\tfrac{1}{3}} \]
Find the inverse of the logarithmic function \( f \).
\[ f(x) = \ln(x) \]
Find the inverse of the exponential function \( f \).
\[ f(x) = e^{x - 1} + 3 \]
Find the inverse of the logarithmic function \( f \).
\[ f(x) = \ln(x + 2) - 3 \]