Question Type 4: Finding inverses for functions that require multiple manipulations Exercises

Find the inverse of $f(x) = \frac{3x + 5}{2x - 1}$.

Find the inverse of the function $f(x) = \frac{2x + 5}{3x}$.

Find $f^{-1}(x)$ for $f(x) = \frac{5x + 7}{2x - 5}$.

Determine $f^{-1}(x)$ for $f(x) = \frac{2x - 3}{x + 4}$.

Compute the inverse of $f(x) = \frac{x - 1}{2x + 3}$.

Find the inverse function of $f(x) = \frac{4x + 1}{x - 2}$.

Find an expression for the inverse function $f^{-1}(x)$ given that $f(x) = \frac{x + 3}{5x - 2}$.

Let $f(x) = \frac{3x - 1}{x} + 2$.

Find an expression for $f^{-1}(x)$.

Determine $f^{-1}(x)$ for $f(x) = \frac{1}{x + 2} - 3$.

Determine the inverse of $f(x) = \frac{3x - 4}{x + 2}$.

Find the inverse of the function $f(x) = \frac{2}{x - 3} + 4$.