Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Exa...

Question

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

Accepted Answer

Hello, everyone. We've been asked to determine G of F of X for the functions F of X equals 12 X plus 64 G of X equals four, X minus 33. I'm going to rewrite this using parentheses. So I have G and then in those parentheses, F of X, this helps me see that I'm going to put the F of X function into the G function. So I now have G and then in parentheses, reading that whole F of X function. So 12 X plus 64 I now know I'm putting 12 X plus 64 in every time I see X in the G function. So what that looks like is four times 12 X plus 64 minus 33. So I want to distribute the four into the parentheses. So four times 12 x is 48 x Plus four times 64 is going to be a 256 minus 33. So for 48 x stays put, I need to combine my 256 and my 33 and that will give me a positive and there's nothing else that can be combined there. So that means G of F Of X is the function 48 x plus 223. So this is part of our solution. We're not done yet. As we also need to find the domain, the domain of G of F of X. As you recall, domain is all the value X values you can plug in that will result in a real number for our function. The main things I check for is there are no square roots. So there's no special case, there, there's no fraction. And if I think about this, if I put a negative number in and multiply it out, I will still get a real number. If I put a positive number in, I will get a real number. So this means my domain is all real numbers. So it's negative infinity to positive infinity. So now that I have both parts I have that G of F of X equals 48 X plus 223. With the domain of all real numbers, I can look at my answer choices and that is answer choice. C have a nice day.

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