Question

Use the following graph of quadratic function f(x)=x2+2x−3 to answer the question. The graph of the function f(x) as described in the problem passing through (-3, 0), (-1, -4) & (1, 0). Which of the following domain restrictions allow an inverse function?There is more than one correct answer. Select all correct answers.

Answer 1

Looking at the graph of f(x), we can see that some values of y have two corresponding values of x.

Since the inverse function changes y with x and vice versa, there will be values of x that will have more than one corresponding value of y, this way it will not be a function.

In order to ensure that f(x) has an inverse function, we need a domain restriction that makes every value of y have only one corresponding value of x.

The domain restrictions that cause every value of y to have only one corresponding value of x are:

x >= -1

x <= -1

0 <= x <= 3

Therefore the correct options are the first, third and fourth options.