Question-161444

Question Number 161444 by cortano last updated on 18/Dec/21

Commented by blackmamba last updated on 18/Dec/21

f (x) = 3 x - 4 \Rightarrow f (2016) = 6044

Commented by blackmamba last updated on 18/Dec/21

f (x) = a x + b

f (x^{2} + x) = {a x}^{2} + a x + b

2 f (x^{2} - 3 x + 2) = 2 [({a x}^{2} - 3 a x + 2 a) + b]

f (x) + 2 f (x^{2} - 3 x + 2) = 3 {a x}^{2} - 5 a x + 4 a + 3 b

{\begin{cases} 3 a = 9 \Rightarrow a = 3 \\ 4 a + 3 b = 0 \Rightarrow 3 b = - 12; b = - 4 \end{cases}

∴ f (x) = 3 x - 4 \Rightarrow f (2016) = 6044

3 \times 2016 - 4

6044.0