Sets, Relations & Functions
Power Functions / Divisors
nta_pyq_2023_jan
Grade 11
Question:
Let $f(x) = 2x^n + \lambda$, $\lambda \in \mathbb{R}$, $n \in \mathbb{N}$, and $f(4)=133$, $f(5)=255$. Then the sum of all the positive integer divisors of $(f(3)-f(2))$ is
Step-by-Step Solution
Key Concept: Subtract equations to get $5^n - 4^n = 61$; solve for $n$, find $\lambda$, then compute $f(3)-f(2)=38$.
$n=3, \lambda=5$. $f(3)-f(2)=2(27-8)=38$. Divisors: $1,2,19,38$; sum $=60$.
Correct Answer: 2