The functions f and g are defined by:

f:x 3x+1
g:x 9-x

Determine an expression for the function gf(x)
3(9-x)+1
27-3x+1

yes, but why not combine the 27 and 1?

3(9-x)+1=27-3x+1

To determine an expression for the composition function gf(x), we need to substitute the expression for g into the function f.

The function g(x) is defined as g:x → 9 - x.

Now, we substitute g(x) into f(x):

f(g(x)) = f(9 - x)

The function f(x) is defined as f:x → 3x + 1.

Substituting g(x) into f, we get:

f(g(x)) = 3(9 - x) + 1

Now, simplify the expression:

f(g(x)) = 27 - 3x + 1

Therefore, the expression for the function gf(x) is:

gf(x) = 27 - 3x + 1.