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The argument of the cosine function must be (2pi/3)*x radians
A function f(x) of the variable x, has a period k where k is some constant, if f(x+ k) = f(x) for every x. It is easy to show that f(x + nk) = f(x) for any integer n. What the above two formulae imply is that the values of the function repeat after an interval (or period) of k. The trigonometric functions are some of the better known periodic functions.
The period of the tangent function is PI. The period of y= tan(2x) is PI over the coefficient of x = PI/2
No. It is an increasing function, with a domain of x > 0. An example of a periodic function is y = sin x. It repeats with every period and keeps crossing, back and forth, over the x-axis. y = log x doesn't behave that way. It just keeps increasing, without limit, as x increases.
The first part of the question is false, and the correct answer is that an even function of minus x equals the function positive x. This follows from the very definition of an even function. The second part of the question is false, because the truth is that the composite function results from taking the function of x within the function g.