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1. On page 27 of the Pearson Edexcel C3 textbook example 13c says "find values of x such that f(x)=f^-1(x)" how did they simplify that to:

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

How can f^-1(x) just become x?
2. (Original post by mp_x)
On page 27 of the Pearson Edexcel C3 textbook example 13c says "find values of x such that f(x)=f^-1(x)" how did they simplify that to:

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

How can f^-1(x) just become x?
f(x) = x is a function that satisfies f(x) = f^-1(x).

http://www.thestudentroom.co.uk/show....php?t=3540817

Or thinking of it graphically, the inverse fuction is a reflection of the function in the line y = x. So only the function y = x could be the inverse of itself.
3. (Original post by mp_x)
On page 27 of the Pearson Edexcel C3 textbook example 13c says "find values of x such that f(x)=f^-1(x)" how did they simplify that to:

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

How can f^-1(x) just become x?
You know that and are simply reflections of one another in the line . So when they give you the equation you know that the solutions to this equation lies on the line allowing you to simplify your equation as .

Examples:

, this one is hard to solve by itself - so let's use the fact that they are inverse functions of one another and satisfy which makes life slightly easier (although not very much so, unless you want to use the Lambert W function).

Here's another one, solve: for - they are inverses of one another and hence satisfy so .
4. (Original post by notnek)
f(x) = x is the only function that satisfies f(x) = f^-1(x).

http://www.thestudentroom.co.uk/show....php?t=3540817

Or thinking of it graphically, the inverse fuction is a reflection of the function in the line y = x. So only the function y = x could be the inverse of itself.
(Original post by Zacken)
You know that and are simply reflections of one another in the line . So when they give you the equation you know that the solutions to this equation lies on the line allowing you to simplify your equation as .

Examples:

, this one is hard to solve by itself - so let's use the fact that they are inverse functions of one another and satisfy which makes life slightly easier (although not very much so, unless you want to use the Lambert W function).

Here's another one, solve: for - they are inverses of one another and hence satisfy so .
I'm still confused sorry
I get that f^-1f(x) = x because you're basically doing something then undoing it but I just don't get how f^-1(x) = x
5. (Original post by Zacken)
You know that and are simply reflections of one another in the line . So when they give you the equation you know that the solutions to this equation lies on the line allowing you to simplify your equation as .

Examples:

, this one is hard to solve by itself - so let's use the fact that they are inverse functions of one another and satisfy which makes life slightly easier (although not very much so, unless you want to use the Lambert W function).

Here's another one, solve: for - they are inverses of one another and hence satisfy so .
I now understand this graphically but not in principle as it doesn't follow the principle in my reply above
6. (Original post by mp_x)
I'm still confused sorry
I get that f^-1f(x) = x because you're basically doing something then undoing it but I just don't get how f^-1(x) = x
The inverse of a function maps the output of the function back to the input.

So if then .

Try it with and :

Now if then it must follow that if then . So this function must be able to "undo" its mapping.

Let's try a function . This clearly won't work because the mapping will always add 1 to the input.

A function can undo it's mapping if it maps any element to itself i.e. the function .

If you're still not sure, please expain the specific part of my post that confuses you.

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Updated: March 28, 2016
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