if f:[1,infinity)-[1,infinity) is defined by f(x)-2^(x(x-1)) then find inverse of f(x)

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- Apr 15th 2011, 11:49 PMprasuminverse
if f:[1,infinity)-[1,infinity) is defined by f(x)-2^(x(x-1)) then find inverse of f(x)

- Apr 16th 2011, 02:31 AMFernandoRevilla
Certainly

**y = f(x)**is strictly increasing in**[1,+infty)**and

**lim_ {x to +infty} f(x) = +infty**

This means that

**f : [1,+infty) -> [1,+infty)**

is bijective, as a consequence there exists**f^{ -1 }**.

Take**log**in both sides of**y = f(x)**, solve the quadratic equation on x and choose the positive branch. - Apr 16th 2011, 02:33 AMchisigma
There is some problem of 'interpretation', so I suppose that the function is...

y= 2^[x (x-1)] (1)

... so that its inverse function is the solution(s) of the equation...

x^2 - x - log2 y=0 (2)

... that are...

x= 1/2 [1 +/- (1+ 4 log2 y)^(1/2)] (3)

It has to be noted that (3) has two distinct brantches and is defined for y> 2^(- 1/4)...

Kind regards

chi sigma