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

Question

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

Accepted Answer

So this problem says for the given functions F of X equals seven x minus one and G of X equals seven X squared. Find f minus G and write the domain. So let's take a look at this. We want to find f minus G. All right questions for F. We know it's seven X -1. We're going to subtract their question for G. Seven X square I had to put them in parentheses. The G just so we remember to distribute are negative to any terms that we have in our equation G since there's only one term here, we don't have to do it once. So we'll have seven X -1. This should be our negative, it's negative seven X squared. I want to rearrange this of my highest degree 1st. We will put -7 x square first Are positive seven x and R -1. Now I'm going to figure out what the domain of this equation is. So if you look at this we want to see if there's any kind of restriction in our equation. Usually restriction would be if we're dividing by a polynomial or if we have the square root in our equation. If you look here, we don't have either of those. So since we have neither of those are domain will just be all real numbers or negative infinity To infinity me our answer with our equation negative seven X squared plus seven X minus one is answer A. Okay, I hope that we solve the problem. Thank you for watching. Goodbye

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

Key Concepts

Function Subtraction

Domain of a Function

Combining Functions

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