Find

Question

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.

$f\left(x\right)=5-x^2$ , $g\left(x\right)=x^2+4x-12$

Accepted Answer

Hello. In this video, we are going to be using the two given functions to find the composite function F minus G and identify its domain. In this problem, we are given F of X is equal to 36 minus X squared. We are also told that G of X is equal to X squared plus 11 X minus seven. So how can we use these two functions to find the composite function F minus G? Well, F minus G is telling us that we want to take the F of X function and subtract the G of X function from it. So we are going to write down our F of X function which is 36 minus X squared and subtract the G of X function from it which will be X squared plus 11 X minus seven. Now, what we want to do is you want to go ahead and simplify this function, we will start by distributing negative one to each term in the G of X function that will allow us to simplify the function to be 36 minus X squared minus X squared minus 11 X plus seven. Now what we want to do is we want to go ahead and combine like terms, we can combine negative X squared and negative X squared. And that will give us negative two X squared 11 X or negative 11 X is our only X term. So we will just list it down as is finally, we can combine 36 and seven together and that will give us a sum of 43. So this means that the simplest form of F minus G is going to be negative two X squared minus 11 X plus 43. Now, what about its domain? We notice that F minus G is in the form of a polynomial function, polynomial functions have a domain of all real numbers. And that means that the domain for this polynomial function will be negative infinity to positive infinity. So F minus G is in the form of negative two X squared minus 11 X plus 43 and its domain is from negative infinity to positive infinity. With that being said, the solution to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.
$f\left(x\right)=5-x^2$ , $g\left(x\right)=x^2+4x-12$

Key Concepts

Function Operations

Domain of a Function

Quadratic Functions

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