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) = x -5, g(x) = 3x²

Accepted Answer

Hello. Today we are given two functions F of X is equal to seven x minus one and G of X is equal to seven X squared. Now we are asked to find F plus G and we are asked to find its domain. So what does it mean to find F plus G? Well, what it means is we're taking our function F which is seven x minus one. And we're going to add our function G which is seven X square to it. So writing that down function F is seven x minus one. And we're going to add our function G which is seven X squared. Now what we need to do is go ahead and simplify this but we can't simplify because there are no combine herbal like terms in this trin Amiel. So instead we're going to go ahead and order the terms with respect to the exponents. So the term with the greatest exponents is seven X squared. Then we are going to write seven X because it's one exponent lower and then negative one because it's a constant. Now, that means that the function F plus G is going to equal to seven X squared plus seven x minus one. But what is the domain of this function while the domain of any polynomial? Because F plus G is a form of polynomial is going to be all real numbers and we represent that as negative infinity to infinity because you could plunge in any number X and you know, it won't break this equation. So again, the domain is going to be all real numbers which is negative infinity to infinity, and this is going to be our function F plus G with its domain. And that means that the answer to this problem is going to be C. 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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