Question

How do you find the domain and range of `f(x)= 2x^2-1`?

Answer 1

Domain: `(-oo, +oo)`
Range: `[-1, +oo)`

Explanation:

Your function is defined for any value of `x`, so you have no restrictions wehn it comes to its domain, which will be `x in RR`, or `(-oo, +oo)`.

In order to determine the function's range, focus on the fact that you're dealing with the square of a value `x`. As you know, for real numbers, the square of any number will be positive.

This means that the minimum value this function can take will occur at `x=0`

`f(0) = 2 * 0^2 - 1 = -1`

For any value of `x !=0`, `f(x)>f(0)`. This means that the function's range will be `[-1, +oo)`.

graph{2x^2-1 [-10, 10, -5, 5]}