Math Problem Statement
Solution
Let's go over the three problems from the image you've uploaded.
Problem 40:
This is a functional equation. The goal is to find . We can try some specific values of to simplify the equation and look for a pattern.
Problem 41:
Here, you are given the value of as a quadratic function in . The task is to find by substituting values and possibly shifting the function.
Problem 42:
Again, this is a functional equation where the goal is to find by solving the equation for different values of .
Would you like me to proceed with solving these step by step? Let me know which one you'd like to start with!
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Math Problem Analysis
Mathematical Concepts
Functional Equations
Algebra
Quadratic Functions
Formulas
f(x) + 3 * f(1/x) = 1/x
f(x+3) = x^2 - 4
2f(x) + f(1/x) = x
Theorems
Properties of functional equations
Quadratic function properties
Suitable Grade Level
Grades 10-12
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