This comes from a math high school contest:
If $$3g(x)+2g(1-x)=9+2x,$$ then what's the value of $g(2)?$
I reached the form $$g(2)=(-2g(-1)+9+2x)/3$$ but I don't know what else to try.
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user376343
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Manuelj
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2$$3g(2) + 2g(-1) = 13.$$ Rinse and repeat, setting $~x = -1.~$ You obtain two linear equations in the two unknowns $~g(2)~$ and $~g(-1).$ – user2661923 Jul 11 '23 at 17:21
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4This (mutatis mutandis) answers your question: If $f(1-x) + 2f(x) = 3x$, what is $f(0)?$ + Please use a more explicit title. – Anne Bauval Jul 11 '23 at 18:52