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) = 3 − x², g(x) = x² + 2x − 15

Accepted Answer

Welcome back. I'm so glad you're here. We are to first find F plus G and then we are to write the domain. So looking at F plus G, what is F? Well, F is F of X equals 12 minus three X squared. And G is G of X equals three X squared minus 18 X plus 27. And in order to add them, we're just going to write down our F of X 12 minus three X squared. And then write plus and now write down our G of X. Three X squared minus 18 X plus 27. Now let's combine like terms we have positive 12 plus 27. That's going to be a positive 39 negative three X squared plus three X squared those cancel out that zero. Now we can just bring down our minus 18 X. Those two aren't like terms, they can't be combined. So that is our F plus G. Now for the domain, we look at what's going on here and we don't have any potential domain restrictions. We don't have a fraction. We don't have absolute value. We don't have a square root so X could be any real number. We write that in interval notation with the parentheses negative infinity, comma, infinity and parentheses. We look at our answer choices and that matches with answer choice. A Well done. We'll catch you on the next one

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

Key Concepts

Function Addition

Domain of a Function

Polynomial Functions

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