In Exercises 31–50, find ƒ+g and determine the domain for each fu...

Question

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

Accepted Answer

Hello. Today we are given two functions F of X is equal to four X plus 15 and G of X is equal to X plus six. We are asked to find F plus G and identify its domain. Well, what does it mean to find F plus G? Well, what this is saying is we're going to take our function F which is four X plus 15 and add a function G which is G of X is equal to X plus six. So writing that down, that's going to be our function F. Which is four X plus 15 plus Our function G which is going to be X plus six. Now, what we need to go ahead and do is simplify this since we are adding these together, we don't need these parentheses here. So I can go ahead and rewrite F plus G as four X plus 15 plus X plus six. Now what I need to do is go ahead and combine the like terms four X and X are combined herbal like terms because four X plus X is going to give me five X and 15 and six are combine herbal because 15 plus six is going to give me 21 this is going to be our function F plus G. F plus G is equal to five X plus 21. Now this represents the function of a line and a line does not have any restrictions in its domain. You can plug in any number of X into this function and you would get exactly one value out. So that means that the domain is going to be the set of all real numbers, which we represent as negative infinity to infinity. And so this is going to be our function F plus G, with its domain being all real numbers. And that means that the answer to this problem is going to be a. So I hope this video helps you in understanding how to find F plus G, including its domain, and I'll go ahead and see you all in the next video.

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