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.