Functions
Functional Equations
JEE Main 2023
Grade 12
Question:
Let $f(x) = 2x^n + \lambda$, $\lambda \in \mathbb{R}$, $n \in \mathbb{N}$. If $f(4) = 133$ and $f(5) = 255$, find the sum of all positive integer divisors of $f(3) - f(1)$.
Step-by-Step Solution
Key Concept: Subtract the two equations to eliminate $\lambda$ and solve for $n$ by testing small integers. Then find $\lambda$, compute $f(3) - f(1)$, and list all its divisors.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 98