XxsciencemathsxX
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Hi!

Can someone please help with with MEI C3 June 2015 Q7 i)?

It says that f(f(x))= x hence write down f^-1(x). Why is f^-1(x)= f(x)?
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Zacken
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(Original post by XxsciencemathsxX)
Hi!

Can someone please help with with MEI C3 June 2015 Q7 i)?

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

In your case, it is clear that ff = ff = \mathrm{id} or ff(x) = ff(x) = x so f is an inverse, i.e f = f^{-1}.
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Notnek
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(Original post by XxsciencemathsxX)
Hi!

Can someone please help with with MEI C3 June 2015 Q7 i)?

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

So if you have ff(x) = x, it must mean that the function is the same as its inverse.


Alternatively you can do this:

Take f^{-1} of both sides to get

f^{-1}ff(x) = f^{-1}(x)

Then f^{-1} and f "cancel" on the left hand side so you're left with

f(x) = f^{-1}(x)
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