Question:medium
Let for some \(\alpha \in \mathbb{R}\), \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function satisfying \(f(x + y) = f(x) + 2y^2 + y + \alpha xy\) for all \(x, y \in \mathbb{R}\). If \(f(0) = -1\) and \(f(1) = 2\), then the value of \(\sum_{n=1}^{5} (\alpha + f(n))\) is:
Let for some \(\alpha \in \mathbb{R}\), \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function satisfying \(f(x + y) = f(x) + 2y^2 + y + \alpha xy\) for all \(x, y \in \mathbb{R}\). If \(f(0) = -1\) and \(f(1) = 2\), then the value of \(\sum_{n=1}^{5} (\alpha + f(n))\) is:
Updated On: Apr 10, 2026
- 110
- 140
- 150
- 170
Show Solution
The Correct Option is C
Solution and Explanation
Was this answer helpful?
0
Top Questions on Functions
- Which of the following statements is true for the function \[ f(x) = \begin{cases} x^2 + 3, & x \neq 0, \\ 1, & x = 0? \end{cases} \]
- CBSE Class XII - 2024
- Mathematics
- Functions
- \( \int_a^b f(x) \, dx \) is equal to:
- CBSE Class XII - 2024
- Mathematics
- Functions
- A relation \( R \) defined on set \( A = \{x : x \in \mathbb{Z} \text{ and } 0 \leq x \leq 10\} \) as \( R = \{(x, y) : x = y\) is given to be an equivalence relation. The number of equivalence classes is:
- CBSE Class XII - 2024
- Mathematics
- Functions
- Find: \[ \int_{\pi/6}^{\pi/3} \frac{\sin x + \cos x}{\sqrt{\sin 2x}} \, dx. \]
- CBSE Class XII - 2024
- Mathematics
- Functions
- Want to practice more? Try solving extra ecology questions todayView All Questions
