Functions (Cambridge International IGCSE Mathematics): Exam Questions

$f(x)=3x--5$

The domain of $f(x)$ is $\{ - 3 , 0 , 2 \}$.

Find the range of $f(x)$.

{ ........................................... }

$\mathrm{f} ( x ) = 7 x - 4$ $\mathrm{g} ( x ) = \frac{2 x}{x - 3} , x \text{eq} 3$ $\mathrm{h} ( x ) = x^{2}$

Find $\mathrm{g} ( 6 )$.

Extract:

f(x) = 7x - 4 g(x) = (2x)/(x - 3), x ≠ 3

Find $fg ( 4 )$.

Extract:

![straight f open parentheses x close parentheses equals 7 x minus 4] ![straight h open parentheses x close parentheses equals x squared]

Find $fh ( x )$.

$f(x)=7-2xg(x)=\frac{10}{x},x\neq0h(x)=27^{x}$

Find

i) $f(-3)$,

ii) $\mathrm{hg}(30)$,

iii) $f^{-1}(x)$.

$f^{-1}(x)=$................................................... [2]

$f(x)=\frac{3}{x+2},x\neq-2$ $g(x)=8x-5$

Work out $\mathrm{g} ( 1 \frac{1}{4} )$.

Extract:

f(x) = 3/(x+2), x ≠ -2

Work out $\mathrm{ff}(2)$.

Extract:

g(x) = 8x - 5

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

Extract:

g(x) = 8x - 5

Find $g^{-1}(x)$.

$g^{-1}(x)=$..................................................

$f$ and $g$ are functions such that

f ( x ) = 2 / x ^2 and g ( x ) = 4 x ^3

Find $f(-5)$

Extract:

f(x) = 2/x^2 and g(x) = 4x^3

Find $fg ( 1 )$.

$\mathrm{f} ( x ) = 2 x - 7$ The domain of $\mathrm{f} ( x )$ is $\{ - 2 , 0 , 5 \}$.

Find the range of $\mathrm{f} ( x )$.

$\{ ........................................... \}$

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

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

Extract:

j(x) = 5^x

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

equation

Find the value of $x$.

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

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

Find $\mathrm{h} ( 4 )$.

Extract:

f(x) = 3x + 2 g(x) = x^2 + 1 h(x) = 4^x

Find $fg ( 1 )$.

Extract:

f(x) = 3x + 2 g(x) = x^2 + 1 h(x) = 4^x

Find $gf ( x )$ in the form $ax^{2}+bx+c$.

Extract:

f(x) = 3x + 2 g(x) = x^2 + 1 h(x) = 4^x

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

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

Extract:

f(x) = 3x + 2

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

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

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

Find in its simplest form

i)$f(x-3)$,

ii)$g(5x)$.

Extract:

f(x) = 4x - 1

Find$f^{-1}(x)$.

$f^{-1}(x)=$ .................................................

Extract:

h(x) = 3^{-x}

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

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

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

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]

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

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

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

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

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

Extract:

f(x) = 4x - 1 g(x) = x^2 h(x) = 3^(-x)

Find $x$ when$f(61)=h(x)$.

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

$h(x)=2^{x}$

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

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

Extract:

h(x) = 2^x

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

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

$h(x)=x^{x},x>0$

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

ii) Find $x$ when $h(x)=256$.

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