Functions: domain, range and compositionEdexcel International A Level Maths: Mind map

Exam questions on Functions: domain, range and composition

1. A function $f$ is defined by $f(x)=x^2-4x+7$, $x\in\mathbb{R}$.
   The domain of $f$ is now restricted to $x\geqslant4$. Find the range of $f$ on this domain.2 marks
2. The functions $f$ and $g$ are defined by $f(x)=2x+3$, $x\in\mathbb{R}$, and $g(x)=x^2-1$, $x\in\mathbb{R}$.
   Solve $\mathrm{fg}(x)=19$.2 marks
3. The functions $f$ and $g$ are defined by $f(x)=\sqrt{x-2}+1$, $x\geqslant2$, and $g(x)=\dfrac{4}{x-1}$, $x\in\mathbb{R}$, $x\neq1$.
   State the range of $f$ and find an expression for $\mathrm{gf}(x)$, stating its domain.3 marks