Amy and her friends have built some functions and they are challenging each other to find the input when they know an output.

They think the inputs to their functions giving the output 10 are 5 for Amy’s function, 4 for Busi’s, $2\frac{1}{2}$ for Chris’s and $5\frac{1}{3}$ for Dudu’s. Do you agree? Why or why not?

Busi says that she goes back in the other direction to find inverses undoing the functions one by one. For her function, to find the input that gives the output 10 she works out $10+2 = 12$ and $12 \div3=4$.

Amy says she uses inverse functions because they undo the operation of a function like undoing your shoelaces. She says that the inverse of her function is $x \to x-5$.

What are the inverse functions for these simple functions?

Can you find the inputs for Amy’s, Busi’s. Chris’s and Dudu’s functions corresponding to an output of 20?

With a partner decide on one of the functions, or build another function of your own. Give each other an output and challenge the other to find the input.  Which of you can do this most quickly and accurately?

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