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

Commented by blackmamba last updated on 18/Dec/21

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

Commented by blackmamba last updated on 18/Dec/21

$$f\left(x\right)=ax+b$$$$f(x^2+x)={ax}^2+ax+b$$$$2f(x^2-3x+2)=2[({ax}^2-3ax+2a)+b]$$$$f\left(x\right)+2f(x^2-3x+2)=3{ax}^2-5ax+4a+3b$$$$\{\begin{array}{l}3a=9\Rightarrow a=3\\ 4a+3b=0\Rightarrow 3b=-12;b=-4\end{array}$$$$\therefore f\left(x\right)=3x-4\Rightarrow f\left(2016\right)=6044$$$$3\times 2016-4$$$$6044.0$$

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