Question

what is the period, domain, range of
f(x)= cos3x + 4sin(1/x^2 -1)

Answer 1

f(x)=cos3x + sin{1/(x^2-1)}

Answer 2

if this has
\[\sin(\frac{1}{x^2-1})\]then since you are not allowed to divide by zero you must make sure that
\[x^2-1\neq 0\] or
\[x\neq \pm1\]

Answer 3

every other number is fine

Answer 4

good.
what about period?

Answer 5

It is not a periodic function

Answer 6

Go to Wolfram and see.

Answer 7

Wolfram says it is not.

Answer 8

And if you examine the graph between -1 and 1 you will see that it is not.

Answer 9

period? not a chance