Functions (Cambridge International IGCSE Maths): Exam Questions

$f(x)=3--2xg(x)=2x+3$

i) Find $f(--3)$.

ii) Find $\mathrm{gf}(--3)$.

Extract:

f(x) = 3 - 2x

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

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

$\mathrm{g} ( x ) = 2 x + 7$ $\mathrm{h} ( x ) = 3 x - 8$

i) Find $\mathrm{gh}(x)$ in its simplest form.

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

$\mathrm{g}^{- 1} ( x )$ ................................................ [2]

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

Find the value of

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

ii) $gf ( 3 )$.

Extract:

g(x) = 1 - 2x

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

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

Extract:

straight h open parentheses x close parentheses space equals space 1 over x comma space x space not equal to 0

Find $x$ when $h(x)=2$.

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

$f(x)=2x+1$ $g(x)=x^{2}+4$

Solve the equation $f(x)=g(1)$.

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

Extract:

f(x) = 2x + 1

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

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

Extract:

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

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

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

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

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

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

Find

i) $\mathrm{f} ( 4 )$,

ii) $hg ( 3 )$,

iii) $\mathrm{g} ( 2 x )$ in its simplest form,

iv) $fg ( x )$, in its simplest form.

Extract:

f(x) = 2x - 3

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

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

Find $\text{gh}(2).$

Extract:

f(x) = 7x - 2

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

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

$f(x)=7+3x$.

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

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

$f(x)=x^{3}g(x)=5x+2$

i) Find $\mathrm{gf}(x)$.

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

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

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

Find $\mathrm{g} ( 1 \frac{1}{2} )$.

Extract:

h(x) = 3 to the power of x

Find $\mathrm{fh}(-1)$.

Extract:

g(x) = 2x - 1

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

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

Extract:

f(x) = 3x + 4

Find $\mathrm{ff}(x)$ in its simplest form.

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

i) Find $\mathrm{gg}(2)$.

ii) Find $g(x+2)$, giving your answer in its simplest form.

iii) Find $x$ when $f(x)=7$.

$x=$............................................... [2]

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

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

$\mathrm{f} ( x ) = 3 x - 2 \mathrm{g} ( x ) = \frac{ 10}{x + 2}$

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

Extract:

f(x) = 3x - 2 g(x) = 10/(x + 2)

Find $gf ( x )$ Simplify your answer.

$g(x)=2x+3h(x)=2^{x}$

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

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

Extract:

straight h left parenthesis x right parenthesis space equals space 2 to the power of x

Find $x$ when $h^{-1}(x)=5$.

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

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

Find the value of $a$.

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

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

Find $fh ( 2 )$.

Extract:

f(x) = 4 - 3x

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

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

Extract:

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

Simplify.

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

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

$f(x)=4x+3g(x)=5x-4$

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

Find the value of $p$.

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

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

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

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

$\mathrm{f} ( x ) = 7 x - 4$

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

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

$f(x)=3x-5$ $g(x)=2^{x}$

Find $fg(3)$.

$g(x)=\frac{10}{x},x\neq0$.

Solve.

$g(2x+1)=4$

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

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

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

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

Extract:

f(x) = 2x - 3 g(x) = 9 - x^2

Solve the equation $gf ( x ) = - 16$.

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

$\text{f}(x)=2x+3$

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

$f(x)=7+3xg(x)=x^{4}$

Find the value of $x$ when $f(x)=g(2)$.

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

$h(x)=ax^{2}+1$

Find the value of $a$ when $h(-2)=21$.

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

$f(x)=3x+4$.

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

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

Calculate $\mathrm{ff}(-3)$

Extract:

f(x) = 5 - 2x g(x) = x^2 + 8

Find

i) $g(2x)$,

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

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

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

Find

i) $\text{hf} ( \frac{8}{3} )$,

ii) $\mathrm{gh}(-2)$,

iii) $g^{-1}(x)$,

$g^{-1}(x)=$ ................................................ [3]

iv) $f^{-1}f(5)$.

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

Find $ff ( 2 )$.

Extract:

f(x) = 7 - x g(x) = 4x + 2 h(x) = 15 - x^2

Find $gf ( x )$ in its simplest form.

Extract:

h(x) = 15 - x^2

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

$f(x)=2x-1$

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

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

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

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

Solve the equation $fg ( x ) = 2$.

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

Find the value of

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

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

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

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

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

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

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

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

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

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

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

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

Simplify, giving your answer as a single fraction.

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

Extract:

h(x) = 27^x

Find $h^{-1}(19683)$.

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

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

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

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

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

Extract:

h(x) = 3 to the power of x

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

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

The diagram shows the graph of $y=\text{f}(x)$ where $\text{f}(x)=x^{2}-\frac{2}{x}-2,x\neq0$.

Use the graph to find

i) $\text{f}(1)$.

ii) $\text{ff}(-2)$.

$h(x)=3^{x}$.

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

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

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

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

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

The functions $f$ and $g$ are such that

$f(x)=5x+3g(x)=ax+b$ where $a$ and $b$ are constants.

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

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

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

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

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

Work out the value of $f^{--1}(3)+f(--0.5)$

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

Simplify $f(2x)+g(x--1)$