# Core 3 Maths Question

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#1
Hi!

It says that f(f(x))= x hence write down f^-1(x). Why is f^-1(x)= f(x)?
0
3 years ago
#2
(Original post by XxsciencemathsxX)
Hi!

It says that f(f(x))= x hence write down f^-1(x). Why is f^-1(x)= f(x)?
A function is said to be an inverse to if , or in more familiar notation . We then say that

In your case, it is clear that or so is an inverse, i.e .
1
3 years ago
#3
(Original post by XxsciencemathsxX)
Hi!

It says that f(f(x))= x hence write down f^-1(x). Why is f^-1(x)= f(x)?
Because (remember an inverse takes you back to the original input).

So if you have , it must mean that the function is the same as its inverse.

Alternatively you can do this:

Take of both sides to get

Then and "cancel" on the left hand side so you're left with

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