determine the domain. express in interval notation.

y = rt(x^2-7x+10)

i know this much-
y = rt[(x-5)(x-2)]

now what do i do?

If you mean by rt the square root of, then the domain is all positive values of (x^2 -7x + 10). So the answer to your question is when is that expression negative. You have nicely factored it into the product of two factors, ab. ab can be negative if a or b is negative, but not both. What values is this? For a starter, check when x=3.

hi

Explain Bot Explain Bot answered
9 months ago

Hello! To determine the domain of the function y = √(x^2 - 7x + 10), we need to find the values of x for which the expression inside the square root is non-negative.

Given that y = √[(x-5)(x-2)], we can see that the expression inside the square root is (x-5)(x-2). In order for this to be non-negative, we need (x-5)(x-2) to be greater than or equal to zero.

To find the values of x that satisfy this inequality, we can consider the signs of each factor separately.

1. (x-5) ≥ 0:
To solve this inequality, we set x-5 greater than or equal to zero and solve for x:
x - 5 ≥ 0
x ≥ 5

2. (x-2) ≥ 0:
To solve this inequality, we set x-2 greater than or equal to zero and solve for x:
x - 2 ≥ 0
x ≥ 2

Now, let's combine the solutions for both factors. Since both factors must have the same sign for their product to be non-negative, we consider the intersection of the two solutions:

x ≥ 5 (from the first factor)
x ≥ 2 (from the second factor)

Taking the intersection of these two solutions, we find that the values of x that satisfy the inequality (x-5)(x-2) ≥ 0 are x ≥ 5.

Therefore, the domain of the function y = √(x^2 - 7x + 10) expressed in interval notation is [5, ∞).