What is the range of the function sqrt(16-x^4)16x4?

1 Answer
Sep 11, 2017

See below.

Explanation:

The minimum value (16 - x^4)(16x4) is 00 for real numbers.

Since x^4x4 is always positive maximum value of radicand is 1616

If including both positive and negative outputs the range is:

[ -4 , 4 ][4,4]

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

Theoretically 'f(x) = sqrt( 16- x^4)f(x)=16x4 is only a function for either positive or negative outputs, not for both.i.e:

f(x) = +- sqrt(16 - x^4 )f(x)=±16x4 is not a function.