Which of the following functions are continuous. Use the appropriate theorems to justify that each function is continuous.

Question

³√(cos x)

x² / √(2 + sin (x))

log₂ |x|

Answer 1

the cube root of any real number is allowed, including negatives.

So the operation is defined on the interval [-1,1] which is the output of the cosine function

the only discontinuity that can possibly happen is when the sine is -2, which CANNOT

happen because the output of the sine function is [-1,1]

the absolute value guarantees the argument of the log function is positive or at least zero.