# Solving problems in function notation

1. Oct 16, 2016

### Daringpear

1. The problem statement, all variables and given/known data
Given that:
g (1)=3
g (2x+1)=4g (x)+x+1

Find g (3)

2. Relevant equations
The awnser is 14. (Taken out of a PSAT workbook)

3. The attempt at a solution
I assume that g(2x+1) refers to a series of transformations (horizontal dilation, up 1) of g(x)
Once g(x) is found, g(3) can easily be solved. The problem is, that I have no idea how to find it.

2. Oct 16, 2016

### pasmith

The second equation tells you how to find $g(2x + 1)$ if you already know $g(x)$.

For which value of $x$ do you already know $g(x)$?

3. Oct 16, 2016

### Staff: Mentor

To me it appears you think a little bit too complicated.
Can you write $3$ as $2x+1$ and what does it tell you about $x$?

4. Oct 16, 2016