Given the functions of f(x)=(x-3)/(x9), g(x)=9x+3, find (gof)(x).
(g◦f) = g(f) = 9f+3
= 9((x-3)/(x9))+3
And you can massage that as you like (whatever x9 means...)
To find the composition of two functions, (gof)(x), we need to substitute the function g(x) into the function f(x).
Step 1: Start with the given functions:
f(x) = (x-3)/(x^9)
g(x) = 9x + 3
Step 2: Substitute g(x) into f(x):
(gof)(x) = f(g(x))
Step 3: Replace x in f(x) with g(x):
(gof)(x) = f(g(x)) = f(9x+3)
Step 4: Substitute g(x) = 9x + 3 into f(x):
(gof)(x) = f(9x+3) = [(9x + 3) - 3]/[(9x + 3)^9]
Step 5: Simplify the expression:
(gof)(x) = (9x)/[(9x + 3)^9]
So, the composition of the given functions is (gof)(x) = (9x)/[(9x + 3)^9].