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Which of the following statements is/are true, based on the Stability Theorem for fixed points of a DTDS with updating function f? Choose all that

Which of the following statements is/are true, based on the Stability Theorem for fixed points of a DTDS with updating function f? Choose all that apply.

If x is a fixed point of the DTDS and |f(x)|<1 then x is a stable fixed point

If f(x)=x and f(x)>1 then x is an unstable equilibrum

If f(x)=x and |f(x)|>1 then x is a root of f

If x is a fixed point of the DTDS and f(x)<1 then x is a stable fixed point

If f(x)=x and |f(x)|>1 then x is an unstable equilibrum

If x is a fixed point of the DTDS and f(x)<0 then x is a stable fixed point

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