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$$2f(x-1)=xf(x)-2x^2+4$$ $$2\left(a\left(x-1\right)+b\right)=x(ax+b)-2x^2+4$$ $$2ax-2a+2b=ax^2+bx-2x^2+4$$ $$0=ax^2-2x^2$$ $$2ax=bx$$ $$-2a+2b=4$$ $$a=2$$ $$b=4$$ $$f(x)=2x+4$$ checking... $$2(2(x-1)+4)=x(2x+4)-2x^2+4$$ $$2(2x-2+4)=2x^2+4x-2x^2+4$$ $$4x+4=4x+4$$ Yay!
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Wed, 16 Apr 2014 10:05 GMT