In Exercises 1–30, find the domain of each function. g(x) = 3/(x-4)

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Hello, today we're going to be finding the domain for the following function. So what we are given is F of X is equal to 17 over X minus 13. Now, one thing to note is that the function is given to us as a rational function. And the general form for a rational function is F of X is equal to one over X. The only value that we are not allowed to have for X in a rational function is zero because if we have a denominator of zero, the function becomes undefined. So what this means is that for a given function, we need to find the restriction for X in order to get the restriction for X, we're going to take our denominator which is X minus 13 in this case. And this denominator cannot equal to zero. We need to go ahead and sell for X. In order to get the restriction for X to sulfur X, we're going to add 13 to both sides of this equation that is going to give us X cannot equal to 13. So what this means graphically is that on the axis, we're going to have a vertical line at the X value X is equal to 13. And this is going to act as a vertical Asymptote to the rational function. And no matter what the shape of the rational function is, we cannot include the value of 13 in our domain. So how do we write the domain in interval notation? While there are two parts to the function that we want to include in our domain, all the values of X coming from negative infinity approaching and all the value of X starting at 13 and approaching positive infinity. So the first portion of the domain is going to include negative infinity. And it's going to stop at 13. Now, since we don't want to include 13 in our domain, we're going to assign it a parenthesis, then we're going to union, the second part of the domain. The second part of the domain starts at 13. But again, since we're not including 13, we're going to assign 13 a parentheses. Then we're going to include all the values of X that come after 13, which is going to go to positive infinity. And this is going to be our domain in Interpol notation. The domain is from negative infinity to 13 union 13 to infinity. And with that being said, the answer to this problem is going to be B So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 1–30, find the domain of each function. g(x) = 3/(x-4)

Verified Solution

Key Concepts

Domain of a Function

Rational Functions

Exclusions in Domain