Question #04a42

1 Answer
Jacob
Nov 25, 2017

#2>=y>=0#

Explanation:

The range of a function is the range of values which the function can take given it's domain.
As the domain is not given, assume that it is all values of x which give a real y (in this case #|\x|<=2#).

Three important facts to remember in this question are that:
a) you can only take the square root of a positive number
b) #y=sqrt(f(x))# only plots the positive square root (principal root)
c) any real number squared #>=0#

Using a), you know #4-x^2>=0#. Because of c), the maximum value #4-x^2# can take is 4, when #x=0#, so the maximum value of y is #sqrt(4)=2#.
Using a) the minimum value #4-x^2# can take is 0, when #x=+-2#, and #sqrt(0)=0#.

Given the minimum and maximum it follows that #0<=x<=2#

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