Edexcel IGCSE Math B 4.F inverse functions

Practise inverse-function questions by replacing the function value with y, rearranging for x and rewriting the result as f inverse.

Exam points

Rearrange a function rule to express x in terms of y before writing the inverse.
Write inverse mappings such as h inverse in the simplest algebraic form.
Check restrictions or domains when the original function includes a condition.

[Maximum number: 3]

Figure 3

Information about the function f is shown in Figure 3.
Given that f is the mapping $\mathrm{f}: x \mapsto a x^{3}+b$ where a and b are constants,

(a)

Using your values of a and b, express the inverse function $f^{-1}$ in the form $f^{-1}:x\mapsto\ldots$ .

[ 2 ]

$y=2x^3+3$ $x=\sqrt[3]{\frac{y-3}{2}}$

Answer:
$f^{-1}:x\mapsto\sqrt[3]{\frac{x-3}{2}}$

Marks: M1, A1.

(b)

Hence write down the inverse function $\mathrm{g}^{-1}$ in the form $\mathrm{g}^{-1}(x)=\ldots$

[ 1 ]

Answer:
$g^{-1}(x)=\frac{px}{x-p}$

Marks: B1.

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