Question

f(x+1)+f(x+2)=2x+3; f(x)=?

Answer 1

Answer:

$F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

Step-by-step explanation:

$1. \mathrm{Subtract\:}f\left(x+2\right)\mathrm{\:from\:both\:sides}\\ F\left(x+1\right)+f\left(x+2\right)-f\left(x+2\right)=2x+3f-f\left(x+2\right)$

$2. \mathrm{Simplify}\\ F\left(x+1\right)=-xf+f+2x$

$3. \mathrm{Divide\:both\:sides\:by\:}x+1;\quad \:x\ne \:-1\\ \frac{F\left(x+1\right)}{x+1}=-\frac{xf}{x+1}+\frac{f}{x+1}+\frac{2x}{x+1};\quad \:x\ne \:-1$

$4. \mathrm{Simplify}\\ F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

Final Answer: $F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$