For the pair of functions defined, find (f/g)(x).Give the domain ...

Question

For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-8

Accepted Answer

Hello everyone. We're going to find the function F over G of X. Given the original functions F of X equals five X minus one, and G of X equals four X plus three. Then we're gonna determine the domain. So I'm gonna rewrite this first with F of X over G of X. So I get five x minus one over four x plus three. And looking at it. There's nothing else I can do with that. So that is my new function. Um Step one of the Solution Pretty Quick. However, I'm not done as I need to find the domain. So I'm going to find the domain of both F of X and G of X first. And then I'll look at the domain of our new function. So F of X. Its domain because there is no fraction and no radical is all real numbers. JIA vacs has the same situation going on. Um There are no fractions. There are no radicals. So it is also all real numbers. However, when we start looking at F over G of X, there is a fraction. So that means that we don't want our denominator to be undefined or equal to zero. So if our denominator can't equal zero, we're gonna find out. When does it equal zero? So do that? We set our denominator equal to zero. So four X plus three. We're gonna set it equal to zero to find out where the hole in the domain is. So we get four X equals negative three, divide by four. So x can't equal negative 3/4. So this means that our domain For f over G of X would be all real numbers, except for -3/4. What this looks like in interval notation is negative infinity to -3/4, Union with negative 3/4 to positive infinity. So that's the other half of our solution. And when I look at my choices, that appears to be answer choice D. Have a nice day.

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For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-8