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Symmetric Relations

35. Let h(x) ...

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35. Let h(x) = f(x)-1 . If f(x)+f(1-x) =2 for all x benlongs to R ,then h(x) is symmetric about

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Q. Let f be a differentiable function such that

f (1) = 2

f^{'} (x) = f (x)

x \in R

h (x) = f (f (x))

h^{'} (1)

f (x) = x^{2} - \frac{1}{x^{2}}

g (x) = x - \frac{1}{x}, x \in R - - 1, 0, 1

h (x) = \frac{f (x)}{g (x)}

then the local minimum value of

h (x)

f

be a differentiable function such that

f (1) = 2

f^{'} (x) = f (x)

x \in R

h (x) = f (f (x))

h^{'} (1)

f (x) = [\frac{x}{[x]}], g (x) = [x [\frac{1}{x}]]

h (x) = [\frac{[x]}{x}],

lim x \to 2^{-} f (x) + lim x \to {\frac{1}{2}}^{+} g (x) + lim x \to 2^{+} h (x) =

f (x) = x^{2} + \frac{1}{x^{2}}

g (x) = x - \frac{1}{x}, x \in R - - 1, 0, 1

h (x) = \frac{f (x)}{g (x)}

, then the local minimum value of the value of

h (x)

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