Solving problems in function notation

[Daringpear]

Homework Statement

Given that:
g (1)=3
g (2x+1)=4g (x)+x+1

Find g (3)

Homework Equations

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

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.

 

[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 $g(x)$?

 

[fresh_42]

Homework Statement

Given that:
g (1)=3
g (2x+1)=4g (x)+x+1

Find g (3)

Homework Equations

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

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.

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 $x$?

 

[Daringpear]

Ah! Your suggestions make sense!

When substituting x for one,

g(2(1)+1)=4g(1)+1+1
g(3)=4(3)+2
g(3)=12+2
g(3)=14