Question

For f(x)= 1/x-5 and g(x)= x^2 + 2 , find (f o g)(x) and find (g o f) (6)? I really need help getting these answers.

Answer 1

(f o g)(x) is same as f(g(x)).
You need to find f(g(x)) for x = 6. So what is f(g(6))?
g(x) = x^2 + 2. Find g(6) ----- Step 1
f(x) = 1/x - 5
f(g(6)) = Substitute g(6) found in Step 1 for x in the equation in the previous line.

Answer 2

So the answer would be 1/33?

Answer 3

Your answer is correct IF \[f(x) = \frac{ 1 }{ (x-5) }\]

But not correct IF
\[f(x) = \frac{ 1 }{ x } - 5\]

Answer 4

It was the first one, so I guess the answer is correct. Thanks! I'm still not sure on the answer to the (f o g)(x) though?

Answer 5

Another way to do it:

\[f(x) = \frac{ 1 }{ (x - 5) }\]
\[g(x) = x ^{2} + 2\]
\[(f o g)(x) = \frac{ 1 }{ ((x ^{2} + 2) - 5) } = \frac{ 1 }{ (x ^{2} - 3) }\]
\[(fog)(6) = \frac{ 1 }{ (6^{2} - 3) } = \frac{ 1 }{ 33 }\]

Answer 6

Do the same for (g o f)(x) for x = 6

Answer 7

Sorry I'm confused right now, was the 1/33 answer for (f o g)(x) or for (g o f)(6)

Answer 8

(f o g)(x) = 1/33 for x = 6

Answer 9

Oh, so for (f o g)(x) they just want me to pick a random number for x and solve and we picked 6?

Answer 10

So if 1/33 is the answer to the first question what is (g o f)(6)

Answer 11

I assumed they meant x = 6 for both parts.
But if not you can leave it as (f o g)(x) = 1/(x^2 - 3)

But you can evaluate (g o f)(x) for x = 6.
But you will have to find (g o f)(x) first. Use the same technique we used earlier.

Answer 12

So the answer would be 3? because 1/6-5 = 1, then 1^2 + 2= 3

Answer 13

Yes it is 3. But don't forget to use parenthesis 1/6 - 5 above should be 1/(6-5) = 1.

Answer 14

Ok, thank you! This is a study guide to a big test this week, so I have a few more questions haha. But thanks for the help on this one!

Answer 15

So I would leave the answers as:
(f o g)(x) = 1/(x^2 - 3)
(g o f)(6) = 3

Answer 16

Sure no problem. Good luck on the tset.

Answer 17

That's what I did, thanks!