A function, f, is the inverse of another , f−1, if:
f(a) = b, and f−1(b) = a.
The domain f−1 is the range of f.
The range of f−1 is the domain of f.
To find the range of a function we have to find the domain of its inverse function.
If two functions are the inverse of each other, their composition is the identity function.
(f o f −1) (x) = (f −1 o f) (x) = x
The graphs of f and f −1 are symmetrical about the bisector of the first and third quadrant.
We must distinguish between the inverse function, f−1(x), and the inverse of a function, .
Calculation of the Inverse Function
1.Write the equation of the function with x and y.
2.Work out the value of the variable x as a function of the variable y.
3.The variables are exchanged.
Calculate the inverse function of:
Check the result for x = 2.