The discussion revolves around finding the domain of the trigonometric function $$f(x) = \frac{1+x}{ e^{cos(x)}}$$. Participants explore the conditions under which the function is defined, focusing on the behavior of the denominator.
Participants generally agree that the function is defined for all real numbers, with no significant disagreement present in the discussion.
No limitations or unresolved mathematical steps are noted in the discussion.
Readers interested in mathematical reasoning related to function domains, particularly in the context of trigonometric and exponential functions.
tmt said:I need to find the domain of this function:
$$f(x) = \frac{1+x}{ e^{cos(x)}}$$
I set $${ e^{cos(x)}}> 0$$
But I'm not sure what to do after this.
Prove It said:The top is obviously defined for all x.
The bottom, as you have established, is always positive. As both cos(x) and e^x are defined for all x, so is their composition.
So the top and bottom are defined for all x. The only place where the quotient of the two functions might not be defined is where the denominator is 0. But you already established that this doesn't happen anywhere.
So what is the domain of your function?
tmt said:All real numbers?