Keywords:
Function, inverse of a function, variable
To find the inverse of a function we must clear the value of the variable x and finally return change.
By definition we have to:
Be a function of the form \(y = f (x)\), the inverse of that function is given by:
\(f ^ {- 1} (y) = f ^ {- 1} (x) = x\)
Then we have the following function:
\(y = f (x)\)
Where \(f (x) = x ^ 2 - 12\)
We clear x:
\(x ^ 2 = y + 12\)
\(x = \pm\sqrt {y + 12}\)
Returning the change we have:
\(f ^ {- 1} (x) = \pm\sqrt {x + 12}\)
Answer:
The inverse function of \(y = x ^ 2 - 12\)is \(f ^ {- 1} (x) = \pm\sqrt {x + 12}\)
