Question

Find the domain and range of the

radical function: f(x)= -√x +1


(radical is only over the x and NOT over the 1).

1. x≤ 0 and y> 1
2. x>0 and y < 1
3. x ≥ 0 and y≤ 1
4. x>0 and y≥ 1

Answer 1

The domain of a radical function is the set of all real numbers for which the radicand (the expression under the radical) is greater than or equal to zero, since the square root of a negative number is not a real number. In this case, the radicand is x, so we need to have x ≥ 0 for the function to be defined.

Therefore, the domain of the function f(x) = -√x + 1 is x ≥ 0.

To find the range of the function, we can consider the behavior of the function as x approaches infinity and as x approaches zero. As x approaches infinity, -√x approaches negative infinity, so -√x + 1 approaches negative infinity + 1 = -∞. As x approaches zero from the right, -√x approaches 0, so -√x + 1 approaches 1.

Therefore, the range of the function is y ≤ 1.

So, the correct option is 3. x ≥ 0 and y ≤ 1.

Answer 2

f(x)= -√x +1x4 which would give you 99