How do you find the domain and range of #f(x) = sqrt(4 - x²)#?

1 Answer
Oct 20, 2015

Answer:

Domain: #[-2,2]#.
Range: #[0,2]#.

Explanation:

Domain: the root is well defined only if its argument is non-negative.

So, we must solve #4-x^2\ge 0#, which leads to #x^2 \le 4#. This inequality holds for #x \in [-2,2]#.

As for the range, we observe that a root is always positive, so since #f(-2)=f(2)=sqrt(4-4)=0#, we have that #0# is the lowest possible value.

Also, we observe that #f(0)=sqrt(4)=2#, and for every other #x# we will have #f(x)=sqrt(4-x^2)#, which means the square root of something less than #4#, as thus something less than #2#. So, #2# is the maximum of the function.