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Question Number 187754 by 073 last updated on 21/Feb/23

Answered by horsebrand11 last updated on 21/Feb/23

$$letf\left(x\right)=ax+b$$$$f(3x+1)=3ax+a+b$$$$f(x-2)=ax-2a+b$$$$f(3x+1)+f(x-2)=4ax-a+2b=10x$$$$\{\begin{array}{l}4a=10\Rightarrow a=\frac{5}{2}\\ -a+2b=0\Rightarrow b=\frac{5}{4}\end{array}$$$$\therefore f\left(x\right)=\frac{5}{2}x+\frac{5}{4}$$$$f\left(3\right)=\frac{15}{2}+\frac{5}{4}=\frac{35}{4}$$

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