Finding Solution to Functional Equation and Verifying by substitution into Functional Equation

Solving the functional equation, f(xy+1) = xf(y) - f(x) + 6, for unknown function f(x) also known as Algebra Analysis in the country of Turkey as a category in Math Olympiad competition.

This problem presented at @SyberMath where the solution f(x)=2x+2 was not verified in original functional equation.

Equating of coefficient and constant terms on LHS and RHS of equation played major role in the solution.

I also want to credit UC Irvine mathematician Zhiqin Lu for his wonderful paper on Functional equations and why functions that are their own inverses work well with them which was noted by Michael Penn as an important simplifying Tool.

[benjaminvatovez]

Thank you for the video.
You can show f(x)=ax+b by putting y=0: f(1)=xf(1)-f(x)+6 then f(x) = f(1) x + 6-f(1). Just rename f(1)=a and 6-f(1)=b as these are constants.