Question

Consider the function f(x) = (x - 3)^2

a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.

Answer 1

Explanation:

a) As the function is a quadratic you could restrict the domain by taking only values either side of the line x = 3. This means the domain will be

a) 3<x<∞

Or

b) -∞<x<3

b) the graph is attached below.

c) The equation of the inverse of f(x) can be found by switching x and y:

X = (y-3)²

√x = y - 3

y = √x + 3

However this takes in positive and negative values of the square root function. So in order to restrict this, we can take the positive square root only.

Thus y = +√x + 3