Following are the graphs of y = sec x, y = esc x, and y = cot x with the spei stricted dom...

Following are the graphs of y = sec x, y = esc x, and y = cot x with the spei stricted domains.

The functions y = cot-1 x, y = sec-1 x, and y = esc= -1 x are not found on a graphing

calculator, but they can be graphed using the relationships mentioned in this

and restated here in parts (a), (b) and (c). Obtain the graphs of these inverse funcU№

using the following information. The graphs of the inverses should be the same as the ones you could find by reflecting the above graphs of the one-to-one functions about the line y = x.

a. For y = sec-3 x, graph y = cos-3 (l/x) using Xmin = -4. Xmax ~ 4, Xscl = 1, Ymin = -1, Ymax = 5.

b. For y = esc-1 x, graph y = sin-1 (l/x) using Xmin = -4, Xmax = 4, Xscl = 1, Ymin = 2, Ymax = 2.

c. For y = cot-1 x, graph y = π/2 – tan-1 x using Xmin = -4, Xmax = 4, Xscl = 1, Ymin = ֊1, Ymax = 5.

Compare the graph of each function with the graph of its inverse function to determine whether the following statements are true or false:

d. If the function is increasing on its domain, then the inverse function is increasing on its domain.

e. If the function is decreasing on its domain, then the inverse function is decreasing on its domain,