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iGCSE (2021 Edition)

4.03 Inverse functions

Interactive practice questions

How can a graphing utility such as a graphing calculator be used to visually determine if two functions are inverses of each other?

We can graph $y=x$y=x on the same axes as the graphs of the two functions and look to see if the graphs intersect on the line $y=x$y=x.

If they do intersect on $y=x$y=x, then they are inverses. If they don't, they are not inverses.

A

We can graph $y=x$y=x on the same axes as the graphs of the two functions and look to see one of the graphs is a reflection of the other about $y=x$y=x.

If they are reflections, then they are inverses. If they aren't reflections, they are not inverses.

B

We look to see if the graphs are reflections of each other about the $y$y-axis.

If they are, they are inverses.

C

We can graph $y=x$y=x on the same axes as the graphs of the two functions and look to see if the graphs intersect on the line $y=x$y=x.

If they do intersect on $y=x$y=x, then they are inverses. If they don't, they are not inverses.

A

We can graph $y=x$y=x on the same axes as the graphs of the two functions and look to see one of the graphs is a reflection of the other about $y=x$y=x.

If they are reflections, then they are inverses. If they aren't reflections, they are not inverses.

B

We look to see if the graphs are reflections of each other about the $y$y-axis.

If they are, they are inverses.

C
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Examine the following graph containing two lines:

Examine the following graph containing two lines:
Examine the following graph containing two lines:

Outcomes

0606C1.1

Understand the terms: function, domain, range (image set), one-one function, inverse function and composition of functions.

0606C1.2B

Use the notation f ^(–1)(x).

0606C1.2C

Use the notation f^2(x) [= f(f(x))].

0606C1.4

Explain in words why a given function is a function or why it does not have an inverse.

0606C1.5A

Find the inverse of a one-one function.

0606C1.5B

Form composite functions.

0606C1.6

Sketch graphs to show the relationship between a function and its inverse.

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