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Question

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

$f\left(x\right)=6x^2-x-1$ , $g\left(x\right)=x-1$

Accepted Answer

Hello. In this video, we are going to be using the two given functions to find the composite function F plus G. The functions given to us are F of X is equal to 11 X squared minus three X minus seven. And the second function given to us is G of X is equal to three X minus four. So how can we use these two functions to find the overall function F plus G? Well, F plus G is telling us that we need to take the F of X function and add G of X to it. So in order to find this composite function, we will use F of X which again is 11 X squared minus three X minus seven and add the G of X function which will be three X minus four. What we will need to do now is we will need to simplify. There are a few terms that we can combine together, we can combine negative three X and positive three X. And these terms will cancel each other out. We can also combine negative seven and negative four, negative seven minus four will leave us with negative 11. So we can simplify this function to be 11 X squared minus 11. This is going to be the simplest form of the composite function F plus G. Now what about its domain? Well, F of F plus G is a polynomial function and polynomial functions always have the domain of all real numbers. So that tells us that the domain is going to be all real numbers which will be negative infinity to positive infinity. So F plus G is equal to 11 X squared minus 11 and its domain will be from negative infinity to positive infinity. With that being said, the solution to this problem is going to be C 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\(\right\))=6x^2-x-1$ , $g\(\left\)(x\(\right\))=x-1$

Key Concepts

Function Operations

Domain of a Function

Rational Functions

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