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Question Number 194190 by tri26112004 last updated on 29/Jun/23

$$ExplanationWhy:$$$$Whilef(ax+b)+f(cx+d)=ex+g$$$$thenf\left(x\right)={Ax}^2+Bx+C¿$$

Commented by Tinku Tara last updated on 30/Jun/23

$$\mathrm{For}\mathrm{the}\mathrm{given}\mathrm{condition}\mathrm{it}\mathrm{is}\mathrm{not}$$$$\mathrm{necessary}\mathrm{for}f\left(x\right)\mathrm{to}\mathrm{be}\mathrm{quadratic}.$$$$f\left(x\right)=Ax+B$$$$f(ax+b)=Aax+Ab+B$$$$f(cx+d)=Acx+Ad+B$$$$g=A(b+d)+2B$$$$e=A(a+c)$$$$A=\frac{e}{a+c}$$$$B=g-\frac{e(b+d)}{(a+c)}$$

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