Question

What is the range of the function `f(x)=x^2-1`?

Answer 1

`{y|y≥-1}`

Explanation:

Basically, we need to find the values `y` can take in `y=x^2-1`.

One way to do this is to solve for `x` in terms of `y`: `x=+-sqrt(y+1)`.

Since `y+1` is under the square root sign, it must be the case that `y+1≥0`. Solving for `y` here, we get `y≥-1`.

In other words, the range is `{y|y≥-1}`.