Question

Give the domain of each of the functions listed below :
a) f(x)= ln (tanh^-1 (x))
b) g(x) = cos ^-1 (e^x)

I just don't know how to set them up to solve for x ...I'm doing a Calc course online on my own, and would really appreciate the help :)
Thanks

Answer 1

a) There can be no log of a negative number or zero, so
tanh^-1(x) > 0
That requires x > 0, since
tanh(x) > 0 for x > 0

b) e^x must be between -1 and 1, since the cosine function is between those extremes.

e^x cannot be <0 for any x
if e^x => 0, x => -infinity
If e^x = 1
x = ln(1) = 0

-infinity < x < 0