Two piece wise functions

Algebra Level 4

If a step function, \(S(x)= \begin{cases} 0 &\text{for} & x \leq 0 \\ 1 &\text{for} & x > 0 \end{cases} \)
Then a piece wise function \(f(x)=\begin{cases} x^2 & \text{for} & 1<x \leq 2 \\ 4x & \text{for} & x > 2 \end{cases}\) can be written in terms of S as \(f(x)=x^2+(ax-x^2)S(x+b)\)
Then, find the value of a+b

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