Find the domain of each function. f(x) = √(24 - 2x)

Question

Accepted Answer

Welcome back. I'm so glad you're here. We are given the function F of X equals the square root of 69 minus X. And we are asked to find the domain. Alright, well we've got a domain restriction here with the square root. Anything inside the radical must be greater than or equal to zero. Why? Because if we have a negative value inside there, then we're going to have imaginary numbers and we don't want that for our domain for X. So how do we find out what values for X would make that inside the radical negative? We're going to set 69 minus 23 X. Or what's inside the radical greater than or equal to zero. And now we're just going to solve for X. So we'll subtract 69 from both sides and then we'll have a negative 23 X is greater than or equal to negative 69. And then we're going to divide both sides by -23. And keep in mind that when we divide both sides by a negative we're going to flip the sign. So it's now going to be X is less than or equal to and that's going to be three over there. So let's look at this on a number line. If we're going from negative infinity all the way to positive infinity and we've got zero somewhere on there. X has to be less than or equal to three. Well here's three, it could be equal to three. So we'll fill that in but it has to be less than or equal to three. So it's going to be heading toward negative infinity. So what are we starting with for putting this in interval notation? We're starting with negative infinity. So we put a parentheses negative infinity comma all the way up to what number 23. And once we get to three it could be three and we express could be three with a bracket. So that means including three. We look at our answer choices and that matches answer choice. A well done, we'll catch on the next one.

Find the domain of each function. f(x) = √(24 - 2x)

Key Concepts

Domain of a Function

Square Root Function

Inequalities

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