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$1-6$ Find $f+g, f-g, f g,$ and $f / g$ and their domains.
$$
f(x)=\frac{2}{x}, \quad g(x)=\frac{4}{x+4}
$$

This question gives us a function g of X, and we know that G of X is equal to negative X squared plus four X plus one. And it wants us to evaluate G of X at negative 1/4. So we're finding g a negative 1/4. I'm gonna start by plugging in what we know. We have negative one negative negative 1/4 squared, plus four times negative. 1/4 plus one. And now I will evaluate. Negative 1/4 squared is gonna be positive. 1/16. Um, and we still to make that negative, so will be left with negative 1/16. We will then add four, um, times negative 1/4 which will just be negative one. And then we add positive one native one plus one is just zero. So we're left with our only other term negative 1/16 so g of negative 1/4 is equal to negative 1/16. And that is your final answer

This question gives you a function and asks you to evaluate it at 10. The function were given is G of X is equal to negative X squared plus four x plus one, and were asked if I n g of 10 first step, of course, is gonna be plugging in 10. Where we have X will have negative 10 square did you notice and putting it in parentheses. That's because it's just a good habit to be in. So we don't confuse negative signs or sometimes will be plugging in more complex expressions. So here we have negative 10 squared plus Fordham samples one 10 squared, obviously, is 100 we're gonna make that negative. So negative 100 plus four times sandwiches 40 plus one. And when we evaluate, this will come out to the answer. That G of 10 is equal to negative 59. And that's your final answer.

This question gives us a function and asks us to solve for a specific value. We have the function G of X, which is equal to negative X squared plus four X plus one, and were asked to find what G is at X equals negative to Sergey of Negative too. The way we'll do that as well. Just plug in negative to anywhere. There's an X could be negative negative two squared plus four times negative, too, plus one and I will evaluate. So I'm going to use, of course, of my order of operations. And first do the exponents. Um, negative two squared is, of course, going to be positive. Four. So we'll have negative times positive for plus four times Negative two plus one will then do all of our multiplication so negative one times four is negative. Four and four times negative. Two is negative. Eight. We'll add one, and then we'll do. Our edition. Make a four plus negative eight is negative. 12 plus positive. One will be negative. 11 so g of negative, too, His negative 11 and that's your final answer

We are given FFX and GFX. So now let's find GF 10. So GF 10 to find this value, we just replace Area X inside the function With 10. Okay, so we have minus Ex replaced with 10 plus four times X, replaced with 10 plus one. So this it goes to minus 10 squared is 100 Plus four times 10 is 40 plus one. Yes, it goes to -159. Okay.