Find ƒ+g and determine the domain for each function. f(x) = √x...

Question

Find ƒ+g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Accepted Answer

Welcome back. I'm so glad you're here. We have two functions F of X and G of X. And we're to find F plus G and then we need to write the domain. Alright, for F plus G, that means we're going to take our F of X function which is the square root of four X. And add that to So plus R. G of X function which is eight X plus 12. Alright, that's F plus G. Now we just need to simplify to combine like terms. So let's simplify with that radical. First the square root of four X is the same as the square to four times the square root of X. The square to four is two and the squared of X is the square root of X. So it's two squared of X. Bring down the rest plus eight X plus 12. Okay. We did the simplification and now combining like terms, Well, none of those are like terms actually. So that is our final answer for F Plus G. Now let's look at the domain for the domain. We look at our two original functions are a five X and our G of X. And we see if there are any potential domain restrictions and there is because we're taking the square root of four X. Whenever we're taking the square root, what's inside the radical needs to be greater than or equal to zero? So in other words this four X needs to be greater than or equal to zero. Why? Because if we have a negative number inside the radical. When we take the square root, we would be dealing with imaginary numbers and we can't have imaginary numbers for our domain. So let's find out what values of X will remain greater than or equal to zero. We'll get X by itself. So we'll divide both sides by four and four, divided by four. On the left is one. So that's just X is greater than equal to zero, divided by four is zero. So X can be any value as long as that is greater than or equal to zero. How do we express that in interval notation? While we put a bracket zero to say, starting with zero including zero, the bracket means including including zero. Starting with zero all the way up to positive infinity. X can be any of those values. We close infinity with the parentheses because we'll never quite obtain infinity. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Find ƒ+g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Key Concepts

Function Addition

Domain of a Function

Combining Domains

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