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IGCSE Math B4.C Function notationTopic Practice

4.C Function notation

Use functional notations of the form f(x) =… and f: x ->…

Question 6(d)

[Maximum number: 5]

The functions f and g are defined as

f:x↦3x−1g:x↦3x,x≠0\begin{aligned} f &: x \mapsto 3x - 1 \\ g &: x \mapsto \frac{3}{x},\quad x \ne 0 \end{aligned}

The function h is such that
h(x)=62x−3.h(x)=\frac{6}{2x-3}.

Solve the equation fh(x)=g(x)

Give your solutions to 3 significant figures.

[ Solutions of ax2+bx+c=0 are x=−b±b2−4ac2a]\left[\text { Solutions of } a x^{2}+b x+c=0 \text { are } x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\right]

॥

Question 6(a)(i)

The functions f, g and h are defined as
f:x↦x+3,g:x↦x2−2x+3,h:x↦6x,x≠0.\begin{aligned} f&:x\mapsto x+3,\\ g&:x\mapsto x^2-2x+3,\\ h&:x\mapsto \frac6x,\quad x\ne0. \end{aligned}

Find

g(-3)

Question 8(a)

[Maximum number: 1]

The functions f and g are defined as

f(x)=2x−5 for all values of x g(x)=x2 for all x⩾0\begin{aligned} & \mathrm{f}(x)=2 x-5 \text { for all values of } x \\ & \mathrm{~g}(x)=x^{2} \text { for all } x \geqslant 0 \end{aligned}

Find f(2)

Question 7(a)

[Maximum number: 1]

The functions f, g and h are defined as

f:x↦x2−2x g:x↦1+2xx≠0 h:x↦5x−4x+3x≠−3\begin{aligned} & \mathrm{f}: x \mapsto x^{2}-2 x \\ & \mathrm{~g}: x \mapsto 1+\frac{2}{x} \quad x \neq 0 \\ & \mathrm{~h}: x \mapsto \frac{5 x-4}{x+3} \quad x \neq-3 \end{aligned}

Find f(-3)

Question 8(b)

The equation of the straight line L is
y=2-3x.

The functions f and g are defined as
f:x↦2−3x,g:x↦3+x1−2x,x≠12.f:x\mapsto2-3x, \qquad g:x\mapsto\frac{3+x}{1-2x},\quad x\ne\frac12.
Find g(-2).

Question 10(c)

[Maximum number: 1]

The function g is such that
g:x↦12x−3.g:x\mapsto\frac{12}{x-3}.

Find h(-9).

Question 9(b)

[Maximum number: 1]

The function f is defined for all values of x by
f:x↦3x2−8,x⩾0.\mathrm f:x\mapsto3x^2-8,\quad x\geqslant0.
The function g is defined by
g:x↦2x2+4x−3,x⩾−1.\mathrm g:x\mapsto2x^2+4x-3,\quad x\geqslant-1.
The function h is defined by
h:x↦3x2+6x−2,x⩾−1.\mathrm h:x\mapsto3x^2+6x-2,\quad x\geqslant-1.

Find f(2).

Question 26(a)

[Maximum number: 1]

The function g is defined by
g:x↦3−5x,x<0.\mathrm g:x\mapsto3-\frac5x,\quad x<0.

Find g(−2)\mathrm g(-2).

Question 11(b)

Here are the functions f, g and h.
f:x↦2x−5,x>1,g:x↦7−8x2x+1,h:x↦2x2+4x−5,x>−1.\begin{aligned}f:x&\mapsto 2x-5,\quad x>1,\\g:x&\mapsto 7-\frac{8x}{2x+1},\\h:x&\mapsto 2x^2+4x-5,\quad x>-1.\end{aligned}

Find the value of g(-1).

Question 11(a)

[Maximum number: 2]

The function f is defined as
f:x↦3x+1x−1.f:x\mapsto\frac{3x+1}{x-1}.

Find f(3)

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