For the pair of functions defined, find (ƒ-g)(x).Give the doma...

Question

For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-6

Accepted Answer

Hello everyone. We're going to find the function F minus G of X. Given the functions F of X equals five X minus one and G of X equals four X plus six. And then we're going to determine the domain of our new function. So knowing that these are subtracted, I'm gonna put F of X in parentheses. So five x minus one then minus my G of X. Also in parentheses four X plus six. I recall when I have a minus sign between parentheses that I can distribute the minus sign in. So I'm going to drop the parentheses on the first one. So the five X minus one and then distribute the minus sign into the second set of parentheses. So minus four X minus six. Now I have some like terms so I'm gonna combine my like terms so five x minus four X. Gives me one X -1 -6 gives me -7. So our new function for f minus G of X Is X -7. So that's the first part of our solution. We're not done quite yet. We need to find its domain. So first we should look at the domains of the original two functions. So the domain of F of X. There is no radical. There is no fraction. The domain, there is all real numbers. Any number you pick that you put in there? That's a real number will give you a solution. The domain of G of X. Um looks like again there's no fractions. There's no radicals. So it is also all real numbers. So finding the domain of F minus G of X And we know that that is X -7. Um there is no fraction, there is no radical, and there is no special domain from the original two. So this is also all real numbers. So our domain is all real numbers, and this looks like it boils down to answer choice B. Have a nice day.

For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.
ƒ(x)=3x+4, g(x)=2x-6

Key Concepts

Function Operations (Addition and Subtraction)

Domain of a Function

Linear Functions

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