Consider the function given by fx 2 sin xx and its graph sh

Consider the function given by f(x) = 2 sin x/x and its graph shown in the figure.

Consider the function given by f(x) = 2 sin x/x and its graph shown in the figure. What is the domain of the function? all real numbers except x = 0 all real numbers except x = 2 all real numbers except x = n pi all real numbers Identify any symmetry of the graph. The graph has no axis symmetry. The graph has x-axis symmetry. The graph has y-axis symmetry. The graph has both y-axis and x-axis symmetry. Describe the behavior of the function as x rightarrow 0. How many solutions does the equation f(x) 2 sin x/x have in the interval [-8,8]? Find the solutions.

Solution

as only (d) part is incomplete,

(d) solution of f(x) is when sin(x)=0 except x=0

therefore, x=n where n is an integer except 0.

therefore solutions are x = -2, -, , 2