Question Type 7: Finding for what value of a given parameter is a function self-inverse Exercises

Find all $b$ such that $f(x) = \frac{x + b + 1}{x + b - 1}$ is its own inverse.

For what value of $b$ is $f(x) = \frac{x + b}{2x + 3 - b}$ self-inverse?

For which value of $b$ is the function $f(x) = \frac{x + b}{x + 1 - b}$ self-inverse?

Determine $b$ such that $f(x) = \frac{b x + 1}{x + b}$ is self-inverse.

Find $b$ so that $f(x) = \frac{x - b}{1 - b x}$ is self-inverse.

Determine $b$ such that $f(x) = \frac{b x + 3}{b - x}$ is its own inverse.

Find $b$ for which $f(x) = \frac{b x + 2}{3x + b}$ satisfies $f(f(x))=x$.

Find $b$ for which $f(x) = \frac{x + 2b}{b x + 1}$ is self-inverse.

Find the value of $b$ so that $f(x) = \frac{x + b}{x - b}$ is its own inverse.

Determine $b$ such that $f(x) = \frac{2x + b}{b x + 2}$ is its own inverse.

For which $b$ is $f(x) = \frac{x - b}{b x + 1}$ its own inverse?