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2.3 Finding the inverse of a function

2 Work out the inverse function for each mapping.
a x → x + 3 b x → x − 8 c x → 4x d x → x
3
3 Work out the inverse function for each equation.
a y = 2x + 5 b y = 4x − 7 c y = x + 1 d y = x −4
2 3
4 Work out the inverse function for each mapping.
x
a x → 5x + 1 b x → 3x − 7 c x → − 10 d x → x + 9
5 4
5 This is part of Mia’s homework.

Question What do you notice about the inverse function of x → 2 − x?
Answer x → 2 − x is the same as x → −x + 2.

x × –1 + 2 –x + 2

x – 2 ÷ –1 – 2 x
–1

x −2 is the same as 2 − x or 2 − x.
−1 1
The inverse function is x → 2 − x, which is the
same as the function.
This function is called a self-inverse function.

a Use Mia’s method to work out the inverse function of each mapping.
i x → 10 − x ii x → 1 − 2x iii x → 4 − x iv x → 3 − 4x
b Which of the functions in part a are self-inverse functions?
6 Harsha thought of a number. She added 13 to the number then multiplied the result by 4.
a Write this as a function as a mapping.
Harsha’s answer was 6.
b Use inverse functions to work out the number Harsha thought of. Show all your working.

Summary

You should now know that: You should be able to:

+ The word ‘algebra’ comes from the word al-jabr. + Use term-to-term and position-to-term rules to
It was first used by the Persian mathematician generate terms of a sequence.

Al-Khwa ¯rizmı ¯, who wrote the first book on algebra. + Derive an expression to find the nth term of an

+ In a non-linear sequence the terms increase, or arithmetic sequence.
decrease, by a different amount each time. + Find the inverse of a linear function.

+ You find the inverse of a function by reversing the
function.

2 Sequences and functions 21