Function and their inverse

Algebra Level 5

f(x)={x+1,    x0(x1)2,x1\large f(x)=\begin{cases} -x+1, \quad \ \ \ \ x \leq 0 \\ -(x-1)^2, \quad x \geq 1 \end{cases}

Define the piecewise function of f(x)f(x) above, find the number of solution(s) of the equation f(x)f1(x)=0f(x)-f^{-1}(x)=0.


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