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Question Number 193267 by Mingma last updated on 09/Jun/23

Answered by cortano12 last updated on 09/Jun/23

$$\left(\mathrm{i}\right)4\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=24\mathrm{x}+5+\frac{6}{\mathrm{x}}$$$$\left(\mathrm{ii}\right)4\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)+\mathrm{f}\left(\mathrm{x}\right)=\frac{24}{\mathrm{x}}+5+6\mathrm{x}$$$$\left(\mathrm{i}\right)\times 4=4\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)+16\mathrm{f}\left(\mathrm{x}\right)=96\mathrm{x}+20+\frac{24}{\mathrm{x}}$$$$\left(\mathrm{i}\right)-\left(\mathrm{ii}\right)$$$$\Rightarrow 15\mathrm{f}\left(\mathrm{x}\right)=90\mathrm{x}+15$$$$\Rightarrow \mathrm{f}\left(\mathrm{x}\right)=6\mathrm{x}+1$$$$\Rightarrow \mathrm{f}\left(337\right)=6\times 337+1=2022+1=2023$$

Commented by Frix last updated on 09/Jun/23

$$f\left(x\right)=18x+1\Rightarrow$$$$4f\left(x\right)+f\left(\frac{1}{x}\right)=72x+5+\frac{18}{x}\ne 24x+5+\frac{6}{x}$$

Commented by Mingma last updated on 09/Jun/23

What's your final answer?

Commented by Tinku Tara last updated on 09/Jun/23

$$15f\left(x\right)=90x+15$$$$\Rightarrow f\left(x\right)=6x+1$$

Commented by Mingma last updated on 09/Jun/23

2023 is correct!

Commented by Mingma last updated on 09/Jun/23

2023 is correct!

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