lean_workbook_plus_60103

Let be $a,b\in \mathbb{R}$ and let be $f: \mathbb{R}\rightarrow \mathbb{R}$ such that $a\cdot f(x)+b\cdot f(1-x)=x\ (1)\ ,\ (\forall)x\in \mathbb{R}$ .\n\ni)Show that $f(x)+f(1-x)=\frac{1}{a+b}\ ,\ (\forall)x\in \mathbb{R}\ ,\ a\neq -b$ ;\n\nii)If $a=b$ , prove that $(\nexists)f$ satisfying $(1)$ ;\n\nii)If $a\neq b$ , find $f$ .