For f(x)= 1/(x-5) and g(x)= x^2+2, find:

a. (f o g)(x)

b. (g o f)(6)

would it be like this for a, and if so how would i continue that?

(f o g)(x)= 1/[(f o g)(x)-5]?

replace x by x^2+2

1/[ (x^2+2) -5 ]

= 1/(x^2 - 3)

b.
f(6) = 1/1 = 1
g(1) = 1+2 = 3

would it be like this for a, and if so how would i continue that?

(f o g)(x)= 1/[(f o g)(x)-5]?
=======================
no, just do what it says

f (g(x))
use g(x) = (x^2+2) for argument of f
in other words
f (x^2+2)
= 1/[ (x^2+2) - 5 ]

Oh okay! That was very helpful. Thank you.

You are welcome :)

To find the composition of two functions, denoted as (f o g)(x), we substitute g(x) into f(x) such that f(g(x)).

a. To find (f o g)(x):

Step 1: Start by finding g(x) by substituting x into the expression g(x) = x^2 + 2:
g(x) = (x^2) + 2.

Step 2: Substitute g(x) into f(x) = 1/(x-5):
f(g(x)) = 1/((x^2) + 2 - 5).

Therefore, (f o g)(x) = 1/((x^2) - 3).

b. To find (g o f)(6):

Step 1: Start by finding f(6) by substituting x = 6 into the expression f(x) = 1/(x-5):
f(6) = 1/(6-5) = 1/1 = 1.

Step 2: Substitute f(6) into g(x) = x^2 + 2:
g(f(6)) = (1)^2 + 2.

Therefore, (g o f)(6) = 1 + 2 = 3.