26 Aug '15 13:217 edits

I want the function of x ( f(x) ) from just one mathematical clue in the form of just one rule about the definite integrals of the curve of the graph for f(x).

All variables/constants here are positive real numbers only.

On the graph for f(x), for some arbitrary constant K where K is some specific x value and where K>0, for any x value that is smaller than K i.e. x<K, then f(x) = 0. But I am not interested here in f(x) for x<K but rather f(x) for x≥K.

The only clue we got what that function is this; if we have a=x1 and b=x2 where a≥K and b≥K and a<b, then the integral of the interval of x from x=a to x=b on that graph is given by:

Κ [a, b] = (K/a) – (K/b)

The only things I have deduce from that clue so far is that the curve for f(x) for x≥K is wholly above the x-axis (thus making all integrals positive ) and that f(x) tends to zero as x tends to +infinity.

But now I am stuck.

So what is the formula for that f(x)?

Any insight will be greatly appreciated.

Not sure but I think I have also deduced, from non-mathematical deduction from its application I have in mind, that:

Κ [K, +∞] = 1

Is that right?

All variables/constants here are positive real numbers only.

On the graph for f(x), for some arbitrary constant K where K is some specific x value and where K>0, for any x value that is smaller than K i.e. x<K, then f(x) = 0. But I am not interested here in f(x) for x<K but rather f(x) for x≥K.

The only clue we got what that function is this; if we have a=x1 and b=x2 where a≥K and b≥K and a<b, then the integral of the interval of x from x=a to x=b on that graph is given by:

Κ [a, b] = (K/a) – (K/b)

The only things I have deduce from that clue so far is that the curve for f(x) for x≥K is wholly above the x-axis (thus making all integrals positive ) and that f(x) tends to zero as x tends to +infinity.

But now I am stuck.

So what is the formula for that f(x)?

Any insight will be greatly appreciated.

Not sure but I think I have also deduced, from non-mathematical deduction from its application I have in mind, that:

Κ [K, +∞] = 1

Is that right?