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

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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.