1. Tardigrade
  2. Question
  3. Mathematics
  4. If f(x + y) = f (x) + 2y2 + kxy and f(a) = 2, f(b) = 8, then f(x) is of the form

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $f(x + y) = f (x) + 2y^2 + kxy$ and $f(a) = 2, f(b) = 8$, then f(x) is of the form

Relations and Functions

Solution:

$f (x + y) = f(x) + 2y^2 + kxy$
$f(1 + y) = 2 + 2y^2 + ky$, putting $x = 1$
putting $y = 1$
$f\left(2\right) = 8 = 2 + 2 + k \Rightarrow k = 4$
$\therefore f \left(1 + y\right) = 2 + 2y^{2} + 4y = 2\left(y + 1\right)^{2}$
$\therefore f \left(x\right) = 2x^{2}$