Question

What will be the value of square root of 9-x^2?

Answer 1

Answer:

Domain: [−3,3]
Range: [−3,0]

Explanation:

In order to find the function's domain, you need to take into account the fact that, for real numbers, you can only take the square root of a positive number.

In other words, in oerder for the function to be defined, you need the expression that's under the square root to be positive.

9−x2≥0

x2≤9⇒|x|≤3

This means that you have

x≥−3  and  x≤3

For any value of x outside the interval [−3,3], the expression under the square root will be negative, which means that the function will be undefined. Therefore, the domain of the function will be x∈[−3,3].

Now for the range. For any value of x∈[−3,3], the function will be negative.

The maximum value the expression under the radical can take is for x=0

9−02=9

which means that the minimum value of the function will be

y=−√9=−3

Therefore, the range of the function will be [−3,0].

graph{-sqrt(9-x^2) [-10, 10, -5, 5]}