Given functions f and g, find (a)

Question

(ƒ \circ g) (x)

and its domain. See Examples 6 and 7.

$ƒ (x) = 8 x + 12, g (x) = 3 x - 1$

Accepted Answer

Hello, everyone. We've been asked to determine F of G of X for the functions F of X equals 12 X plus 64 and G of X equals four, X minus 33. We also need to find the domain of F of G of X. I want to rewrite this with parentheses. So it's F and then I'm opening the parentheses and putting G F X inside of it. I do this because it's a little easier for me to see what I'm plugging in. I now can see that the G of X function is going into the F of X function. So I'm gonna say it's F of, and then my G of X function is four X minus 33. So I now know that I'm putting four X minus 33 in for X in that F of X function. So that would be 12 times four X - plus 64 Distributing the 12 into the parentheses. 12 times four, X is 48, X 12 times a negative 33 is a negative 396 plus 64. I need to combine my like terms. I have nothing to combine with the X terms of 48 x stays put and then it's minus 332. So my F of G of X function Is 48 X -332. So this is part of our solution. We do need to still find the domain. So our domain here again, recall a domain is that all the values that will make the function come out to be a real number. So we don't want any imaginary numbers. In this case, I don't have any radicals. I don't have any fractions. I have the ability to plug in any real number and it should come out. So both positives and negatives, decimals, it all should work. So our domain is all real numbers. So it goes from negative infinity to positive infinity. So now that we know the domain, we know that F of G of X equals 48 X minus 332 with the domain of all real numbers. And that's answer choice. A have a nice day.

Given functions f and g, find (a) $(ƒ \circ g) (x)$ and its domain. See Examples 6 and 7.
$ƒ (x) = 8 x + 12, g (x) = 3 x - 1$

Key Concepts

Function Composition

Domain of a Composite Function

Linear Functions

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