Question

Can someone explain to me why my book's answer to the question, "For what values of x is f(x) > 0" is [0, ∏︎/2) ∪︎ (3∏︎/2,5∏︎/2) ∪︎ (7∏︎/2, 4∏︎] and not 0, 2∏︎, and 4∏︎? Is the question not asking for values of x where y is greater than zero?

Answer 1

See explanation

Explanation:

Question "For what values of x is f(x) > 0" means that you should determine the values of x for which corresponding value of f(x) is greater than 0.

The graph of the given function is placed above the x-axis and below the x-axis.

Points at which the graph intersects the x-axis are x-intercepts (or zeros of the function). For these values of x, f(x)=0.

f(x)>0 when the graph is above the x-axis (all corresponding values of y or f(x) are positive).

The diagram shows that the graph of f(x) is above the x-axis for all

`x\in \left[0,(\pi)/(2)\right)\cup \left((3\pi)/(2),(5\pi)/(2)\right)\cup \left((7\pi)/(2),4\pi\right]`

At
`x=0,\ 2\pi,\ 4\pi` the function f(x) gains it maximum value of 4.