(a) For what range of v is the function f(x) = x in Hilbert space, on...

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(a) For what range of v is the function f(x) = x" in Hilbert space, on the interval (0. 1)? Assume v is real, but not necessarily positive. (b) For the specific case v = xf (x)? How about (d/dx)f (x)? 1/2, is f(x) in this Hilbert space? What about (a) For what range of v is the function f(x) = x" in Hilbert space, on the interval (0. 1)? Assume v is real, but not necessarily positive. (b) For the specific case v = xf (x)? How about (d/dx)f (x)? 1/2, is f(x) in this Hilbert space? What about