In Exercises 1–30, find the domain of each function. f(x) = √(x -...

Question

In Exercises 1–30, find the domain of each function. f(x) = √(x - 3)

Accepted Answer

Hello today we're going to find the domain for the given function. So the function given to us is F. Of X. Is equal to the square root of the quantity three X minus 12. Now let's just quickly recall how we find the domain of a square root function. If we are given a square root function so F. Of X is equal to the square root of X. Keep in mind that the only values of X that don't work with this function are going to be any negative values. So X must be greater than or equal to zero. With that being said. Every time you want to find the domain of a square root function, you take the inside argument and set it greater than or equal to zero. So what we're going to do is take our inside argument inside the square root and that's going to be three X -12. And we're going to set that greater than or equal to zero. Now we need to go ahead and solve for X. In order to simplify this quantity inequality. So in order to do that, we're gonna go ahead and add 12 to both sides of this inequality. Doing so is going to give me three X greater than or equal to and two sulfur X. We're just gonna divide both sides of the inequality by three. And we're going to get X is greater than or equal to four. Now how do we represent this in interval notation? Well let's go ahead and draw this on a number line real quick. So the value that we're looking at is for on the number line, and X is going to be all the values that are greater than four, but also include for because X can equal for as well. So the way that's gonna look is the value for and all the values that come after it. So the way that we represent that is we're including four in the set of solutions or in this case of bracket with four. And we want all the values greater than four. Or in other words, we want everything that comes after four, which is going to be positive infinity. And this is going to be the domain of our given function. That And that means that the solution to this problem is going to be be. So I hope this video helps you in understanding how to find the domain of a square root function. And I'll go ahead and see you all in the next video.

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