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This is a broad question that depends on the function. Let's look at simple linear ones and you can get some idea. Say f(x)=2x+3
We can write this as y=2x+3.
Now solve for x and we have (y-3)/2=x
so f(y)=(y-3)/2 and this is the inverse function.
We solved for the other variable and wrote the function in terms of it.


So if we have a the point 2 in the original function, f(2)=2x2+3=7
Now f(7) in the inverse gives us (7-3)/2=4/2=2.


For a point (a,b) if f(a)=b, then if g is the inverse g(b)=a.

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