# In Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see.63. a. y = tan-1 (tan x)          b. y = tan (tan-1 x)64. a. y = sin-1 (sin x)            b. y = sin (sin-1 x) 65. a. y = cos-1 (cos x)             b. y = cos (cos-1 x)

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In Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see.

63. a. y = tan-1 (tan x)          b. y = tan (tan-1 x)

64. a. y = sin-1 (sin x)            b. y = sin (sin-1 x)

65. a. y = cos-1 (cos x)             b. y = cos (cos-1 x)

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Step 1

Since you have submitted three questions, we'll answer the first question. For the other questions please submit the questions again and specify it.

a) Domain of y = tan-1 (tan x) will depend on the domain of tan x. That is all real numbers except ± {pi/2 , 3pi/2 , 5pi/2 , ..... }

Range of y = tan-1 (tan x) will depend on the range of tan^-1 x. That is ( - pi/2 , pi/2 )

Step 2

b) Domain of y = tan(tan^-1 x) will depend on the domain of tan^-1 x. That is all real numbers.

Range of y = tan-1 (tan x) will depend on the range of tan x. That is all real numbers.

Step 3

Graph y=tan^-1(tanx) using graphing calculator.

This graph makes sense because the function is not valid for x= ± {pi/2 ,...

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