f ( x ) = a x + b \text { for } 1 \leq x < 2
Solve for x
\left\{\begin{matrix}\\x\in [1,2)\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&(b=0\text{ and }f=a)\text{ or }(f=0\text{ and }a=0)\\x=\frac{bf}{f-a}\text{, }&f\neq a\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f\in \mathrm{R}\text{, }&\left(x=0\text{ and }b=0\right)\text{ or }\left(a=0\text{ and }x=b\right)\text{ or }\left(x\geq 1\text{ and }x<2\right)\\f=\frac{ax}{x-b}\text{, }&x\neq b\end{matrix}\right.
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