Question

Consider the function y = √4-x.
What are the domain and range of this function?

Answer 1

For the function y = √4-x, we know that the value inside the square root must be non-negative. Therefore, we have the inequality:

4 - x ≥ 0

Solving for x, we get:

x ≤ 4

So the domain of the function is all real numbers less than or equal to 4.

For the range, we know that the square root of any non-negative number is always non-negative. Therefore, the smallest value that y can take is 0, which occurs when x = 4. As x decreases, y increases without bound. So the range of the function is [0,∞).

Explanation: