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Question Number 131332 by ZiYangLee last updated on 03/Feb/21

$$\mathrm{If}f\left(x\right)\mathrm{is}\mathrm{a}\mathrm{function}\mathrm{defined}\mathrm{for}\mathrm{all}\mathrm{real}\mathrm{numbers}$$$$\mathrm{such}\mathrm{that}f\left(2x\right)=x+f\left(x\right)\mathrm{and}f\left(1\right)=2,$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}f\left(64\right).$$$$[\mathrm{Ans}:65]$$

Answered by mr W last updated on 03/Feb/21

$$f\left(2\right)=1+f\left(1\right)=1+2=3$$$$f\left(4\right)=2+f\left(2\right)=2+3=5$$$$f\left(8\right)=4+f\left(4\right)=4+5=9$$$$f\left(16\right)=8+f\left(8\right)=8+9=17$$$$f\left(32\right)=16+f\left(16\right)=16+17=33$$$$f\left(64\right)=32+f\left(32\right)=32+33=65$$

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