Functions (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

$\mathrm{g}\left(x\right)=2x+3\mathrm{h}\left(x\right)=2^x$

Find $x$ when $\mathrm{gg}\left(x\right)=7$.

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

Find $x$ when ${\mathrm{h}}^{-1}\left(x\right)=5$.

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

$\mathrm{f}\left(x\right)=3x^2+a$  where $a$ is an integer. $\mathrm{f}\left(-2\right)=19$

Find the value of $a$.

$a=$ ................................................ 

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

Find  $\mathrm{fh}\left(2\right)$.

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

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

Simplify.

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

[2]

ii) $\mathrm{gf}\left(x\right)-9\mathrm{g}\left(x\right)$

[4]

$\mathrm{f}\left(x\right)=4x+3\mathrm{g}\left(x\right)=5x-4$

$\mathrm{fg}\left(x\right)=20x+p$

Find the value of $p$.

$p=$ .................................................. 

$\mathrm{h}\left(x\right)=\frac{5x-1}{3}$

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

${\mathrm{h}}^{-1}\left(x\right)=$ .................................................. 

$\mathrm{f}\left(x\right)=7x-4$      

Find the value of $x$ when $\mathrm{f}\left(x+2\right)=-11$.  

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

$f\left(x\right)=3x-5$      $g\left(x\right)=2^x$

Find $fg\left(3\right)$.

$\mathrm{g}\left(x\right)=\frac{10}{x},x\ne 0$.  

Solve.

$\mathrm{g}(2x+1)=4$

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

$\mathrm{f}\left(x\right)=2x-3\mathrm{g}\left(x\right)=9-x^2$  

Find $x$ when  $5\mathrm{f}\left(x\right)=3$.

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

Solve the equation  $\mathrm{gf}\left(x\right)=-16$.

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

$\text{f}\left(x\right)=2x+3$  

Find $\text{f}(1-x)$ in its simplest form.

$\mathrm{f}\left(x\right)=7+3x\mathrm{g}\left(x\right)=x^4$  

Find the value of $x$ when  $\mathrm{f}\left(x\right)=\mathrm{g}\left(2\right)$.  

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

$\mathrm{h}\left(x\right)=a{x}^2+1$

Find the value of $a$ when $\mathrm{h}(-2)=21$.  

$a$ = ............................................... 

$\mathrm{f}\left(x\right)=3x+4$.  

Find  ${\left(\mathrm{f}\left(x\right)\right)}^2$  in the form  $a{x}^2+bx+c$.

$\text{f}\left(x\right)=5-2x$         $\mathrm{g}\left(x\right)=x^2+8$

Calculate $\mathrm{ff}(-3)$

Find 

i) $\mathrm{g}\left(2x\right)$,

[1]

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

${\mathrm{f}}^{-1}\left(x\right)=$.............................................. [2]

$\mathrm{f}\left(x\right)=8-3x$        $\mathrm{g}\left(x\right)=\frac{10}{x+1},x\ne -1$         $\mathrm{h}\left(x\right)=2^x$

Find

i) $\mathrm{hf}\left(\frac{8}{3}\right)$,

[2]

ii) $\mathrm{gh}(-2)$, 

[2]

iii) ${\mathrm{g}}^{-1}\left(x\right)$,

${\mathrm{g}}^{-1}\left(x\right)=$ ................................................ [3]

iv) ${\mathrm{f}}^{-1}\mathrm{f}\left(5\right)$.

[1]

$\mathrm{f}\left(x\right)=7-x$      $\mathrm{g}\left(x\right)=4x+2$      $\mathrm{h}\left(x\right)=15-x^2$

Find $\mathrm{ff}\left(2\right)$.

Find $\mathrm{gf}\left(x\right)$ in its simplest form.

Find $\mathrm{h}\left(2x\right)$ in its simplest form.

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

$\mathrm{g}\left(x\right)=\frac{3}{x+4}$

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

Find $\mathrm{gf}\left(x\right)$.

Write your answer in the form $\frac{a}{bx+c}$.

Solve the equation $\mathrm{fg}\left(x\right)=2$.

$\mathrm{g}\left(x\right)=1-2x$ 

Find the value of 

Find $\mathrm{g}\left(x\right)\mathrm{g}\left(x\right)-\mathrm{gg}\left(x\right)$, giving your answer in the form $a{x}^2+bx+c$.

$\mathrm{j}\left(x\right)=5^x$.

Find $x$when ${\mathrm{j}}^{-1}\left(x\right)=2$.

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

$\mathrm{h}\left(x\right)=3^x$.

Find the value of $k$ for which $\frac{1}{\mathrm{h}\left(x\right)}=9^{kx}$

      $k=$ ................................................ 

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

Find $\frac{\mathrm{g}\left(x\right)}{\mathrm{f}\left(x\right)}+x$.
Give your answer as a single fraction, in terms of $x$, in its simplest form.

$\mathrm{h}\left(x\right)=x^2$

Find the values of $p$ that satisfy $\mathrm{h}\left(p\right)=p$.

$\mathrm{f}\left(x\right)=7-2x\mathrm{g}\left(x\right)=\frac{10}{x},x\ne 0\mathrm{h}\left(x\right)={27}^x$

Simplify, giving your answer as a single fraction.

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

Find  ${\mathrm{h}}^{-1}\left(19683\right)$.

$\mathrm{h}\left(x\right)=3^x$.

Find $x$ when ${\text{h}}^{-1}\left(x\right)=-2$.

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

$\text{gg}\left(x\right)=a{x}^4+b{x}^2+c$    Find the values of $a$, $b$, and $c$.   

$a$ = ....................................................
$b$ = ....................................................
$c$ = ....................................................

Find $x$ when $\text{hf}\left(x\right)=81.$   

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

The diagram shows the graph of $y=\text{f}\left(x\right)$ where $\text{f}\left(x\right)=x^2-\frac{2}{x}-2,x\ne 0$.

Use the graph to find

i) $\text{f}\left(1\right)$.  

[1]

ii) $\text{ff}(-2)$.  

[2]

$\mathrm{h}\left(x\right)=3^x$.

If  $\mathrm{h}\left(3x\right)=k^x$, find the value of $k$.  

$k$ = ................................................ 

$\mathrm{g}\left(x\right)=2x-1\mathrm{h}\left(x\right)=3^x$

Find  $x$ when  $h^{-1}\left(x\right)=g\left(2\right)$.  

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

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 $b$.

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

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

$\mathrm{f}\left(x\right)=\frac{2x}{5}-1$

Work out the value of  ${\mathrm{f}}^{–1}\left(3\right)+\mathrm{f}(–0.5)$

$\mathrm{f}\left(x\right)=5-x$  and     $\mathrm{g}\left(x\right)=3x+7$

Simplify $\mathrm{f}\left(2x\right)+\mathrm{g}(x–1)$