Write (f ∘ g)(x) as an expression in terms of X

Question

f(x) = 2-x/x+1

g(x) = 18-3x

(f ∘ g)(x) = Answer

Answer 1

Hello Mike!

(f ∘ g)(x) means that we're going to plug g(x) (which is 18-3x) into f(x) in place of x.

(f ∘ g)(x) --> f(g(x))

If g(x) = 18 - 3x, then we're looking for f(18-3x).

Meaning we're going to plug in (18-3x) every time we see an x in the original f(x) = (2-x)/(x+1)

f(18 - 3x) = (2 - [18 - 3x])/([18 - 3x] +1) Now we simplify, distributing the negative in the numerator.

f(18 - 3x) = (2 - 18 + 3x)/ (18 - 3x +1) Now we combine like terms within the numerator and the same in the denominator.

f(18 - 3x) = (-16 + 3x) / (19 - 3x) Now here is where we check to see if there's a common factor we can take out of everything to simplify our faction, but there is no factor (aside from 1, which wouldn't change anything) we can take out of each term. So this is our final answer!

Just to be clear, the answer should be that

(f ∘ g)(x) = (-16 + 3x)

(19 - 3x)

Hope this helps! :)