Composite functions

Question

I have a few questions on composite functions. 

 

f(x)=x-6, g(x)=5x+6 find (g of f)(x)    5

 

Answer 1

When you're composing functions together, you will plug the second function into the first in place of x. Here, you have

(gºf)(x) = g(f(x))

g(x) = 5x+6

f(x) = x-6

Plug in f(x) in place of x

g(f(x)) = 5(x-6)+6

 

Now we just need to distribute and simplify:

g(f(x)) = 5x-30+6

g(f(x)) = 5x-24