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

Question

1563 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-11T15:16:32

See below.

The minimum value $(16 - x^4)$ 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:

$[ -4 , 4 ]$

For positive output $[ 0 , 4 ]$
For negative output $[ -4 , 0 ]$

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

$f(x) = +- sqrt(16 - x^4 )$ is not a function.

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