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Mayran F.

Precalculus

1 week, 5 days ago

how to determine the domain of a combination of functions

Georgia State University

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how to determine the domain of a combination of functions

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Video Transcript

for this question we are going to talk about the domain of a combination of functions. When you're combining more than one function to create a new function, you have to take into account domain restrictions from each individual function. Yeah, for example, let's say we have F of X is equal to x minus four and G of X is equal to the square root of X plus five. Well ffx has no domain restriction. The domain is all real numbers. G fx has a domain restriction because the radic hand has to be greater than or equal to zero. X plus five has to be greater than or equal to zero. Which means X has to be greater than or equal to negative five. When we combine functions, let's just say we simply add the two functions. Okay then the domain restriction has to include all restrictions on the individual functions. And since one of those functions had a restriction, the combination has that restriction as well. Mm Now be careful because if we were going to do something like F of X over G fx. Now we create an additional domain restriction. The original domain restriction of X greater than or equal to negative five still applies. But now we've created a solution where the denominator cannot equal zero. So we have a new restriction to take into account which adjusts the previous one instead of X being greater than or equal to negative five. Now X cannot equal negative five because Of the denominator. And we would have to say X is greater than negative five