The problem involves function notation and seeks to determine the value of g(3) given specific function properties and an equation relating g(2x+1) to g(x). The subject area is primarily focused on function transformations and evaluations.
The discussion has progressed with participants offering insights into how to manipulate the equation to find g(3). Some guidance has been provided regarding substituting specific values into the equation, and there is a recognition of the logical steps involved in reaching a solution.
Participants note that the problem is derived from a PSAT workbook, which may impose certain constraints or expectations on the problem-solving approach. There is an acknowledgment of the initial confusion regarding the transformations involved in the function.
To me it appears you think a little bit too complicated.Daringpear said: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.