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

$\mathrm{g}\left(x\right)=1-2x\mathrm{h}\left(x\right)=\frac{1}{x},x\ne 0\mathrm{j}\left(x\right)=5^x$

Find $\mathrm{hh}\left(x\right)$, giving your answer in its simplest form.

Find $\mathrm{j}\left(5\right)$.

   $\mathrm{j}\left(x\right)=\mathrm{hg}\mathit{(}-12\mathit{)}$

Find the value of $x$.

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

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

Find $\mathrm{h}\left(4\right)$.

Find $\mathrm{fg}\left(1\right)$.

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

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

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

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

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

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

Find in its simplest form

i)$\mathrm{f}(x-3)$,

[1]

ii)$\mathrm{g}\left(5x\right)$.

[1]

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

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

Find the value of$\mathrm{hh}\left(1\right)$, correct to 4 significant figures.

$\mathrm{g}\left(x\right)=8x-5\mathrm{h}\left(x\right)=x^2+6$

i) Show that $\mathrm{hg}\left(x\right)=19$ simplifies to $16x^2-20x+3=0.$  

[3]

ii) Use the quadratic formula to solve $16x^2-20x+3=0.$
Show all your working and give your answers correct to 2 decimal places.  

$x=$......................... or $x=$......................... [4]

$\mathrm{f}\left(x\right)={\left(x-1\right)}^2-4$ for $x\ge 1$

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

Find $\mathrm{gf}\left(2\right)$.

Find ${\mathrm{f}}^{-1}\left(x\right)$ and state the the domain of ${\mathrm{f}}^{-1}\left(x\right)$.

Solve $\mathrm{f}\left(x\right)=\mathrm{g}\left(x\right)$.

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

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

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

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

Show that$\mathrm{g}(3x-2)-\mathrm{h}(-3)$ can be written as $9x^2-12x-23$.

Find $x$ when$\mathrm{f}\left(61\right)=\mathrm{h}\left(x\right)$.

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

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

Solve the equation $h^{-1}\left(x\right)=0.5$.

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

$\frac{1}{\mathrm{h}\left(x\right)}=2^{kx}$ Write down the value of $k$.

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

$\mathrm{h}\left(x\right)=x^x,x>0$

i) Calculate $\mathrm{h}(0.3)$. Give your answer correct to 2 decimal places.

[2]

ii) Find $x$ when $\mathrm{h}\left(x\right)=256$.

$x=$............................................... [1]