+118654 The inverse of
\(f(x) \qquad is \qquad f^{-1}(x)\)
Don't get this confused with a power of -1 it is not the same at all.
The inverse function is the reflection of the function in the line y=x
You have to be a bit careful though becasue it must still be a function which means domain restrictions often have to be imposed.
ex
Consider the function
\(f(x)=x^2-4\)
this will only have an inverse if you resrtrict the domain to either x>0 or x<0
I've chosen to restrict it to x>0
so
if
\(f(x)=x^2-4 \qquad where \qquad x>0\\ then\\\)
to find the inverserse function we do this
change f(x)to y and then make x the subject, then swap the x and y over.
\(y=x^2-4 \qquad x\ge0\\ y+4=x^2\\ x=\sqrt{y+4}\\swap\\ y=\sqrt{x+4}\\ \text{putting the function notation back again}\\ f^{-1}(x)=\sqrt{x+4}\)
This is the working of the graph if you want to look at it properly
https://www.desmos.com/calculator/3f3ldenjwr
and
Here are the graphs
I know that you didn't ask for all that stuff but hopefully you will learn from it anyway :)
