Question
Asked Jan 15, 2020
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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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Expert Answer

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 ) 

 

 

Calculus homework question answer, step 1, image 1
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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.

Calculus homework question answer, step 2, image 1
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Step 3

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

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

Calculus homework question answer, step 3, image 1
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