Pre-Calculus Question HELP?

Question

Using exponential and logarithmic functions, determine a real valued function for:
The inverse of tanh(x)

Answer 1

1/tanh(x)= ((e^2x)+1)/((e^2x)-1)

Answer 2

i might say shape is a factor of engineering meaning that an outstanding hold close on math is considerable, pre-cal is is like algebra to the subsequent point with the Pi chart and understanding approximately radians and attitude measures (which seems considerable) yet Calculus is the learn of derivatives, (the slope of a line at a undeniable component) style of pointless no rely what field of workd your going to, in case you inquire from me.

Answer 3

That is easy.....

tanh(x) = t = (exp(x)-exp(-x))/(exp(x)+exp(-x))

exp(x) - exp(-x) = t [exp(x) + exp(-x)]
exp(x) - exp(-x) = t exp(x) + t exp(-x)
collect terms in exp(x) and exp(-x)
(1 - t)exp(x) = (1 + t)exp(-x)
divide both sides by exp(-x)
(1-t) exp(2x) = 1+ t
divide by 1-t
exp(2x) = (1 + t)/(1 - t)
take the natural logarithm
2x = Ln[(1 + t)/(1 - t)]

x = 0.5 Ln[(1+t)/(1-t)]

QED

Answer 4

tanhx=y= (e^x-e^-x)/(e^x+e^-x) If you put e^x=z and solve it for x
x=1/2ln[(y+1)/(y-1)] or interchanging x and y

arTh x = 1/2ln[(x+1)/(x-1)]