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Raman · 2011-04-13, 17:31

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, x^y 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 = z^z, 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...

2011-04-13, 17:31	#1
Raman Noodles "Mr. Tuch" Dec 2007 Chennai, India 4E9₁₆ Posts	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, x^y 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 = z^z, 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