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Old 2011-04-13, 17:31   #1
Raman
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"Mr. Tuch"
Dec 2007
Chennai, India

4E916 Posts
Default Inverse of functions

That website http://wims.unice.fr contains a plenty of useful online calculators,
really a lot, but I couldn't find out a place where inverse of functions is being sought.

For example take up with 1. e^x + sinh(x)
Can put with sinh(x) = \frac{e^x - e^{-x}}{2} and then solve with that quadratic for e^x.
The inverse is being given by ln (\frac{x\pm\sqrt{x^2+3}}{3})

2. cosh(x) + sinh(x)
The inverse of this function is given by ln\ x
just simply this case goes away within that way.
3. cos(x)+sin(x)
Writing with this function as \sqrt{2}\ sin(x+\frac{\pi}{4})
The inverse can be given by sin^{-1}\frac{x}{\sqrt 2}-\frac{\pi}{4}

OK, then what will be the inverses of these following functions?
It seems that they cannot be solved by using all those elementary mathematical functions at all!
(4) x^x
(5) x^{\frac{1}{x}}
(6) x+sin(x)
(7) x+tan(x)
(8) x+e^x
(9) e^x+sin(x)
(10) sin(x)+sinh(x)

Thanks for your help, if possible within any case

Disclaimer:
I had faced a problem which asked me to give an algorithm to check out if N is a perfect power, xy where that value of y is ≥ 2. I told that it can be done by using checks of \sqrt{x}, log_2(x), ^3\sqrt{x}, log_3(x), ^4\sqrt{x}, log_4(x), ... alternately, what value to check upto for base? Till N = zz, for some value of z. Thus, how to write up with that value of z as a function of N? How does that way work out rather...

Last fiddled with by Raman on 2011-04-13 at 17:56
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