Given f(x) = ex – e-x , find f-1(x)?

Question

Inverse Functions

Answer 1

If you mean f(x) = e^x -e^(-x) , you might find the answer in the following link

Answer 2

hypersine of x sinh(x) = (e^x - e^-x)/2, so your equation f(x)=2*sinh(x). The inverse function for sinh(x) = arcsinh(x) = log(x+sqrt(x^2+1))

In your equation we try f^-1(x) = log(.5x+sqrt(.25x^2+1)),
to accommodate the factor of two.

Since by definition f(f^-1(x))=x, plug the above value into your equation and you will find that e^y-e^-y with y=log(.5x+sqrt(.25x^2+1)) will give x as the answer.

(Edited 7/16)

Answer 3

besides the actuality that it says the f"(x) is (ie: f"(3)) you may only plug the three into all the different x's, because it delivers what x equals. then only sparkling up it like an time-honored challenge.

Answer 4

exp(x) - exp(-x) = 2 * sinh(x) = f(x) = y

x = f_inv(y) = arcsinh(y/2)

rewriting in x:
f_inv(x) = asinh(x/2)

asinh is the excel function for arcsinh

Answer 5

Your notation is not clear to me... but I'm guessing - 1/2ex

Answer 6

ef-1 -ef+1
f=0

Answer 7

y=ex-e-x
y=(e-1)x-e
(y+e)/(e-1)=x
f^-1(x)=(x+e)/(e-1)