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

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Answer 1 · 2017-04-02T13:41:14

${y|y≥-1}$

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 ${y|y≥-1}$ .

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