Inverse functions and their graphsEdexcel International A Level Maths: Mind map

Exam questions on Inverse functions and their graphs

1. The function $f$ is defined by $f(x)=\dfrac{2x+1}{x-3}$, $x\in\mathbb{R}$, $x\neq3$.
   Find the value of $f^{-1}(5)$.2 marks
2. The function $g$ is defined by $g(x)=x^2-6x+5$, $x\geqslant3$.
   Explain why $g$ has an inverse function with the domain $x\geqslant3$, but would not have one if the domain were $x\in\mathbb{R}$.2 marks
3. The function $f$ is defined by $f(x)=2\mathrm{e}^{x}-5$, $x\in\mathbb{R}$.
   Find $f^{-1}(x)$ and state its domain.3 marks