Composite and inverse functionsEdexcel A-Level Maths: Mind map

Exam questions on Composite and inverse functions

1. The functions $f$ and $g$ are defined by $f(x)=3x-2$, $x\in\mathbb{R}$, and $g(x)=x^2+1$, $x\in\mathbb{R}$.
   Solve the equation $fg(x)=49$.2 marks
2. The function $h$ is defined by $h(x)=\frac{2x+1}{x-3}$, $x\in\mathbb{R}$, $x\neq3$.
   Find the value of $h^{-1}(5)$.2 marks
3. The function $f$ is defined by $f(x)=x^2-4x+7$, $x\geq2$.
   Express $f(x)$ in the form $(x-a)^2+b$ and hence state the range of $f$.3 marks