You're give that f(x) is a linear function, so let f(x) = ax + b.SolXero said:Homework Statement
Given f[f(x)] = 2x + 1 find all linear functions that satisfy this identity.
Given f[f[f(x)]] = 2x + 1 find all linear functions that satisfy this identity.
2. The attempt at a solution
I have not started to attempt a solution at this because I have no idea how to do these types of problems.
A linear function is a mathematical function that can be represented by a straight line on a graph. It has the general form y = mx + b, where m is the slope of the line and b is the y-intercept.
Identifying the correct linear functions that satisfy a given identity is important in order to accurately model and predict real-world phenomena. This can be used in various fields such as economics, engineering, and physics.
One common strategy is to plug in different values for the variables in the given identity and solve for the missing variable. Another strategy is to use the slope-intercept form to determine the slope and y-intercept of the linear function.
Sometimes, the given identity may not have enough information to determine a unique linear function. In other cases, the identity may have multiple solutions, making it difficult to determine the correct one.
Technology, such as graphing calculators or software, can be used to graph the given identity and visually identify the linear function that satisfies it. This can also be used to check the accuracy of hand-calculated solutions.