In Exercises 51–66, find a. (fog) (x)b. (go f) (x)c. (fog) (2)d. ...

Question

In Exercises 51–66, find a. (fog) (x)b. (go f) (x)c. (fog) (2)d. (go f) (2). f(x) = 1/x, g(x)= 1/x

Accepted Answer

So this problem says to solve F M G 1/5 were f of X is equal to X over X plus five MG X is equal to two over x minus five. So let's go ahead and rewrite our F F G of X M F G of X. This is the same thing as saying F on the outside, G f X on the inside. So if you write this again, I'm gonna take what we have for G F X and plug it into the X. F of X. So that is like saying we have two over x -5 and for X now we will write out our equation of a fix. We substitute October X -5. We get two over X -5, divided by two over X minus five. And then plus five. Like so I want to simplify this equation. We get two over X months, file on top the bottom, we just get two over X. Now some of five and further, I want to get rid of this fraction on the bottom. Let's multiply everything by the reciprocal reciprocal of the denominator is X over two. Since I'm multiplying on the bottom, I have to multiply on the top or else it's not allowed. We have to multiply something by one and this X over two over X over two is equal to one. So we do that, We get two over X two x times x over two minus five times X over 2/2 over X times X over two. We get two X over two X minus five X over two Over two X over two x. Find even further We get 1 -5 x over two Over one which is just 1 - x over two. This is our equation of death of G. F. X. Numbers here are X is actually equal to one fits so we're gonna take that one fits and substitute it in for X. I write, write this again, I get f of G of 1/5. This is equal to 1 -5 times one fits over two. Let's write out even further one minus you have five times 1/ which is 1/2. This is just equal to one half. So the answer to our equation is 1/2 or answer b. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 51–66, find a. (fog) (x)b. (go f) (x)c. (fog) (2)d. (go f) (2). f(x) = 1/x, g(x)= 1/x

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