Functions (Edexcel IGCSE Maths A: Higher): Exam Questions

$\mathrm{f}\left(x\right)=3x^2—2x—8$

Express $\mathrm{f}(x+2)$ in the form $a{x}^2+bx$

The functions $\mathrm{f}$ and $\mathrm{g}$ are such that $\mathrm{f}\left(x\right)=x+3$     and       $\mathrm{g}\left(x\right)=\frac{1}{x-2}$

Find $\mathrm{fg}\left(x\right)$
Give your answer as a single algebraic fraction expressed as simply as possible.

Express the inverse function ${\mathrm{g}}^{-1}$ in the form ${\mathrm{g}}^{-1}\left(x\right)=...$

The function $\mathrm{f}$ is such that

$\mathrm{f}\left(x\right)=4x—1$

Find ${\mathrm{f}}^{-1}\left(x\right)$

The function $\mathrm{g}$ is such that

$\mathrm{g}\left(x\right)=k{x}^2$ where $k$ is a constant.

Given that $\mathrm{fg}\left(2\right)=12$

work out the value of $k$

The functions $\mathrm{f}$ and $\mathrm{g}$ are such that

$\mathrm{f}\left(x\right)=3x-1\mathrm{and}\mathrm{g}\left(x\right)=x^2+4$

Find ${\mathrm{f}}^{-1}\left(x\right)$

Given that $\mathrm{fg}\left(x\right)=2\mathrm{gf}\left(x\right)$,

show that $15x^2-12x—1=0$

The function f is defined as

$\mathrm{f}\left(x\right)=\frac{x-6}{2}$

Find f (8)

Express the inverse function ${\mathrm{f}}^{-1}$in the form ${\mathrm{f}}^{-1}\left(x\right)$ = ......

The function $g$ is defined as

$g\left(x\right)=\sqrt{x-4}$

Which values of $x$ cannot be included in a domain of $g$?

Express the function $\mathrm{gf}$ in the form $\mathrm{gf}\left(x\right)$= .......

Give your answer as simply as possible.

$\mathrm{f}\left(x\right)=\frac{3}{x+1}+\frac{1}{x-2}$

State one value of $x$ which cannot be included in any domain of f.

Find the value of f(0)

Find the value of $x$ for which $\mathrm{f}\left(x\right)=0$

Show clear algebraic working.

 The diagram shows parts of the graphs of $y=\mathrm{f}\left(x\right)$and $y=g\left(x\right)$. 

 Find g(0) 

 Find $\mathrm{g}$f(–1) 

$\mathrm{f}\left(x\right)=\frac{2}{x}$

$\mathrm{g}\left(x\right)=\frac{x+1}{x}$

State which value of $x$cannot be included in the domain of f or $g$.

Solve $\mathrm{gf}\left(a\right)=3$

Express the inverse function ${\mathrm{g}}^{-1}$ in the form ${\mathrm{g}}^{-1}\left(x\right)$

f:$x$ → 2$x^2$$+$1  $\mathrm{g}$:$x$→ $\frac{2x}{x-1}$ where $x$≠ 1

Express the composite function gf in the form $\mathrm{g}$f:$x$ → .....

Give your answer as simply as possible.

Express the inverse function ${\mathrm{g}}^{-1}$in the form ${\mathrm{g}}^{-1}:x$→ ......

The functions $\mathrm{g}$ and h are defined as

$\mathrm{g}\left(x\right)=\frac{x}{2x-5}$

$\mathrm{h}\left(x\right)=x+4$

Find the value of $\mathrm{g}$(1)

State which value of $x$ must be excluded from any domain of $\mathrm{g}$

Find $\mathrm{gh}\left(x\right)$

Simplify your answer

Express the inverse function ${\mathrm{g}}^{-1}$ in the form ${\mathrm{g}}^{-1}\left(x\right)$ = .....

$\mathrm{f}\mathit{\left(}\mathit{x}\mathit{\right)}=\frac{2x}{x\mathit{-}1}$

Find the value of $\mathrm{f}\left(11\right)$

State which value of $x$must be excluded from any domain of f

Find ${\mathrm{f}}^{-1}\left(x\right)$

State the value which cannot be in any range of f

f is the function such that

$\mathrm{f}\left(x\right)=\frac{x}{3x+1}$

Find f(0.5)

Find ff(−1)

Find the value of $x$ that cannot be included in any domain of f

Express the inverse function ${\mathrm{f}}^{-1}$ in the form ${\mathrm{f}}^{-1}\left(x\right)$= ......

Show clear algebraic working.

The function f is such that $\mathrm{f}\left(x\right)=x^2–8x+5$ where $x⩽4$ Express the inverse function ${\mathrm{f}}^{-1}$ in the form ${\mathrm{f}}^{–1}\left(x\right)=...$

${\mathrm{f}}^{–1}\left(x\right)=................$

Two functions, $\mathrm{f}$ and $\mathrm{g}$ are defined as

$$\begin{gathered} \mathrm{f}:x\mapsto 1+\frac{1}{x}\mathrm{for}x>0 \\ \mathrm{g}:x\mapsto \frac{x+1}{2}\mathrm{for}x>0 \end{gathered}$$

Given that $\mathrm{h}=\mathrm{fg}$
express the inverse function ${\mathrm{h}}^{-1}$ in the form ${\mathrm{h}}^{-1}:x\mapsto ...$

${\mathrm{h}}^{-1}:x\mapsto$..................... 

$\mathrm{f}\left(x\right)=2x-3$ and $\mathrm{g}\left(x\right)=x^2$

Show that  ${\mathrm{f}}^{-1}\left(55\right)=\mathrm{f}g\left(4\right)$

$\mathrm{f}\left(x\right)=\frac{x}{3}+4$  for all values of $x$.

$\mathrm{g}\left(x\right)=6x^2+3$ for all values of $x$.

Work out $\mathrm{fg}\left(x\right)$.

Give your answer in the form $a{x}^2+b$   where $a$ and $b$ are integers.

$\mathrm{f}\left(x\right)=3x^2–4x+8$ for all values of $x$

Jenny says,

“f(10) must equal 2 × f(5), because 10 is 2 × 5”

Is Jenny correct? Show working to support your answer.

$\mathrm{g}\left(x\right)=16–x\mathrm{h}\left(x\right)=x^3$

Solve    $\mathrm{gh}\left(x\right)=24$

$\mathrm{f}\left(x\right)=\frac{x}{x+2}\mathrm{g}\left(x\right)=x^2–2$

Work out $\mathrm{fg}\left(x\right)$

Give your answer in the form    $a+b{x}^n$    where $a,b$ and $n$ are integers.

$\mathrm{f}\left(x\right)=\frac{2x+3}{x-4}$

Work out ${\mathrm{f}}^{–1}\left(x\right)$

$\mathrm{g}\left(x\right)=3x+7$

Solve  ${\mathrm{g}}^{–1}\left(x\right)=2x$

$x$ = ....................

A function machine is shown below.

If the Input is 3, the Output is 5.

If the Input is 7, the Output is 25.

Use this information to fill in the two boxes.

$\begin{array}{rcl}\mathrm{f}\left(x\right)& =& cx+d\\ \mathrm{f}\left(4\right)& =& 7\\ \mathrm{f}\left(10\right)& =& 22\end{array}$

Work out the values of $c$ and $d$.

$c=$.........................

$d=$.........................

The functions $\mathrm{g}$ and $\mathrm{h}$ are such that

$\mathrm{g}\left(x\right)=\frac{11}{2x-5}$

$\mathrm{h}\left(x\right)=x^2+4x⩾0$

What value of $x$ must be excluded from any domain of $\mathrm{g}$?

Solve $\mathrm{gh}\left(x\right)=1$

The functions $\mathrm{f}$ and $\mathrm{g}$ are such that

$$\begin{gathered} \mathrm{f}:x\mapsto 5x+7 \\ \mathrm{g}:x\mapsto \frac{5}{2x-9} \end{gathered}$$

State which value of $x$ cannot be included in any domain of $\mathrm{g}$

Find $\mathrm{fg}\left(4\right)$

The function $\mathrm{h}$ is such that

$\mathrm{h}:x\mapsto 3x^2-12x+8$ where $x>2$

Express the inverse function ${\mathrm{h}}^{-1}$ in the form ${\mathrm{h}}^{-1}:x\mapsto ....$

Show that $\frac{x^2+3x}{2x^2+5x-3}$ can be written as  $\frac{x}{kx-1}$

State the value of $k$.

$\mathrm{f}\left(x\right)=\frac{x}{2x-1}$

Find the inverse function $\mathrm{f}{}^{-1}$  in the form $\mathrm{f}{}^{-1}\left(x\right)=.......$

Show your working clearly.

The functions $\mathrm{f}$ and $\mathrm{g}$ are such that

$\mathrm{f}\left(x\right)=5x+3\mathrm{g}\left(x\right)=ax+b$ where $a$ and $b$ are constants.

$\mathrm{g}\left(3\right)=20\mathrm{and}{\mathrm{f}}^{-1}\left(33\right)=\mathrm{g}\left(1\right)$

Find the value of $a$ and the value of $b$.

$\mathrm{f}\left(x\right)=\sqrt{x-6}$

Find f(10)

State which values of $x$ must be excluded from a domain of f

The diagram shows part of the graph of $y=\mathrm{g}\left(x\right)$

Find $\mathrm{g}\left(2\right)$

Find $\mathrm{fg}\left(0\right)$