Composite and inverse functionsAQA A-Level Maths: Mind map

Exam questions on Composite and inverse functions

1. The functions $f$ and $g$ are defined for all real $x$ by $f(x)=3x-2$ and $g(x)=x^2+1$.
   Solve $fg(x)=13$.2 marks
2. The function $h$ is defined by $h(x)=\dfrac{2x+1}{x-3}$ for $x\in\mathbb{R}$, $x\neq3$.
   Given that $h^{-1}(a)=5$, find the value of $a$ without finding $h^{-1}(x)$.2 marks
3. The function $f$ is defined by $f(x)=(x-2)^2+3$ for $x\ge2$.
   State the range of $f$ and find $f^{-1}(x)$.3 marks