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

1 Answer
KillerBunny
Oct 20, 2015

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.

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