Question

Find range of f(x).

Answer 1

\[f(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}\]

Answer 2

one can find the domain of inverse function\[x=\frac{e^y - e^{-y}}{e^y+ e^{-y}}\]

Answer 3

how u got that invverse

Answer 4

thats the start point, replacing x and y and solving for y

Answer 5

and maybe there are some shorter ways than that considering that\[f(x)=\tanh x\]

Answer 6

I don't know ABCD of hyperbolic functions. :(

Answer 7

ok so the first method will be a good approach

Answer 8

just note that\[x=\frac{e^{2y} - 1}{e^{2y}+1}\]\[e^{2y}=\frac{-x-1}{x-1}\]\[2y=\ln (\frac{-x-1}{x-1})\]

Answer 9

can u find the domain of this function?

Answer 10

\[\frac{-x-1}{x-1} > 0 , x \neq 1\]

Answer 11

right and what will be final answer?

Answer 12

x < -1

Answer 13

\[x \in (-\infty,-1)\]

Answer 14

how did u get that?

Answer 15

I put -x-1 > 0

Answer 16

be careful :)

Answer 17

u should put\[\frac{-x-1}{x-1}>0\]

Answer 18

oops sorry,
\[x \in (-1,1)\]

Answer 19

quite right, we are done

Answer 20

This is range ?

Answer 21

yes range of original function
http://www.wolframalpha.com/input/?i=range+of+tanh+x

Answer 22

Ah, great thanx!!

Answer 23

yw :)