(Fixed-point property) Show that if f is continuous on [0, 1] and 0 < f(x)<1 for all x e [0, 1], then there ex- ists at least one point c in [0, 1] at which f(c) = c. HINT: Apply the intermediate-value theorem to the function g(x) =x – f(x).

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A: (I) For x=-1: LHL=limx→-1-f(x)        =limx→-1-1        =1 RHL=limx→-1+f(x)        =limx→-1+(-x)…

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A: Given that: f(x) is continuous function on [a,b], differentiable function on (a,b),