Of the choices given, which value is NOT in the domain of the function?

Question

Of the choices given, which value is NOT in the domain of the function f(x)=(cosx)^x?

a)1
b) pi/2
c)4pi/3
d) 4 e) 2pi

can anyone explain to me how to do this?
thankyou!

thats what i thought at first but it has to be one of them since there isn't a choice. thanks for you response

i dont understand santamann please explain why it has to be greater then 0

Answer 1

The domain of a function can be given as any subset of the maximum possible domain, which is all the values of the variable for which the function would be defined. In this case no limiting domain is given so we must assume the maximum domain. Both cos and power function are defined for all positive x, so I can't see how any of these answers can be correct.

Later edit having seen answer below. Cosx being negative still doesn't cause any problem. A negative number can be raised to a power and give a real number.

Answer 2

The base of the exponential must be positive or can be zero if the exponent is positive
cos1 =0.54 ok
cospi/2=0 exponent is positive ok
cos4pi/3<0 NO
cos 4<0 NO
cos 2pi = 1 ok.
c and d are NOT in the domain

Answer 3

The domain is all the values that x can have. I can not see any value of x that is not valid except, possibly, for d) 4 e) 2pi because I do not understand what it means.

No matter what value you put in for x, cos(x) cannot be greater than 1 nor less than -1. When you raise any number in this range to any value of x, you get a valid repsonse.