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Composite Functions

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https://vle.mathswatch.co.uk/images/questions/question17183.png

May 19, 2018

#1
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a)

As the rule states, we first add 4, then multiply the sum by 2.

The first imput gives us 6, we follow the fuction's rules:

6 + 4 = 10, 10 * 2 = 20

The output, or y, is 20.

The second part, gives us the output. We can just reverse it.

What times 2 is 13? 13/2 = 6.5.

What plus 4 is 6.5? 6.5 - 4 = 2.5.

The imput is 2.5.

The first blank is 20.

The second blank is 2.5.

I hope this helped,

Gavin

May 19, 2018
#2
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b)

In mathematics, an inverse function (or anti-function) is a functionthat "reverses" another function.

The function the problem gives us is basically: y = x/5 + 1

To inverse it, we write it in the form, x = ...

First we subtract 1 from both sides, to get y - 1 = x/5

Then we multiply both sides by 5, we get: 5y - 5 = x

It becomes, x = 5y - 5, or x = 5(y-1)

So the function is subtract one, then multiply the difference by 5.

I hope this helped,

Gavin

May 19, 2018