What is the range of the function sqrt(16-x^4)?

Sep 11, 2017

See below.

Explanation:

The minimum value $\left(16 - {x}^{4}\right)$ is $0$ for real numbers.

Since ${x}^{4}$ is always positive maximum value of radicand is $16$

If including both positive and negative outputs the range is:

$\left[- 4 , 4\right]$

For positive output $\left[0 , 4\right]$
For negative output $\left[- 4 , 0\right]$

Theoretically '$f \left(x\right) = \sqrt{16 - {x}^{4}}$ is only a function for either positive or negative outputs, not for both.i.e:

$f \left(x\right) = \pm \sqrt{16 - {x}^{4}}$ is not a function.