I ran across this question and am not sure of the answer. Needless to say, I'm having trouble with conceptualizing all of the facets of functions.

The question is: Investigate and understand f(2x - 1) = x + 4

I get two different possible answers -

- Let z = 2x - 1
- x = (z + 1)/2; Evaluating for x
- f(z) = x + 4; from the original function statement
- f(z) = [(z + 1)/2] + 4; Substituting for x from step 2
- f(2) = [(2 + 1)/2] + 4; Evaluating with z = 2
- f(2) = 3/2 + 4
- f(2) = 3/2 + 8/2 = 11/2

BUT

- Let g(x) = 2x-1
- f(g(x)) = x + 4; Composition of 2 functions
- g(2) = 2(2) - 1 = 3; Evaluating with g(2)
- f(g(2)) = 3 + 4 = 7

No? What did I miss here? Am I misunderstanding a fundamental concept in functions?