If $f: R \rightarrow R$ is defined as $f(x+y)=f(x)+f(y), \forall x, y \in R$ and $f(1)=10$,then,$\sum_{r=1}^n(f(r))^2=$
- A$\frac{7}{2} n(n+1)$
- B$5 n(n+1)$
- C$\frac{50}{3} n(n+1)(2 n+1)$
- D$\frac{100}{4} n^2(n+1)^2$
Explore More
Similar Questions
Let $f$ be a function defined by $f(xy) = \frac{f(x)}{y}$ for all positive real numbers $x$ and $y$. If $f(30) = 20$,then $f(40) = $
If $f(x)$ is a polynomial function satisfying the condition $f(x) \cdot f(1/x) = f(x) + f(1/x)$ and $f(2) = 9$,then:
Let $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a function from $\mathbb{Z}$ to $\mathbb{Z}$ defined by $f(x) = ax + b$ for some integers $a$ and $b$. Determine the values of $a$ and $b$.
Medium
View SolutionLet $f$ be a function such that $f(x + y) = f(x) + f(y)$ for all $x$ and $y$,and $f(x) = (2x^2 + 3x)g(x)$ for all $x$,where $g(x)$ is continuous and $g(0) = 3$. Then $f'(x)$ is equal to:
If $f(a) = a^2 + a + 1$,then the number of solutions of the equation $f(a^2) = 3f(a)$ is:
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo