Question

Look at the function f(x) = x2 + 3. Which of the following describes the domain and range of the function and its inverse?

Answer 1

The third option is the closest option available.

Explanation:

The domain includes all real numbers, while the range only includes values that are greater than or equal to 3 (since f(0) = 3 ).

To find out the details for the inverse, we need to find the inverse itself.

So, to do this, let's quickly substitute y for f(x).

`f(x)=x^2+3` becomes
`y=x^2+3`.

Now, we switch the positions of x and y, like so:
`x=y^2+3`.

Now, we solve for y.

`x=y^2+3\\x-3=y^2\\√(x-3)=y`

So, the inverse is
`y=√(x-3)`.

This particular equation only provide valid outputs for all values of x that are greater than or equal to 3. So its domain includes all numbers greater than or equal to 3.

The third option is the closest option available.