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

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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