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Let f(x)=tan^-1x. Then the domain of f(x) is all real numbers and the range is [-π/2, π/2].

True or False? 

 Mar 21, 2020
 #1
avatar+402 
+1

This is true, as the domain of arctan can accept any real number. the range however is limited to [-pi/2, pi/2] so it is continuous and 1-1 as a function.

 Mar 21, 2020
 #2
avatar+18926 
+2

The range does not include the two limit values  -pi/2  and  pi/2.

The range should be expressed as ( -pi/2, pi/2 )

using the round brackets to indicate that the endpoints are not included.

 Mar 21, 2020
 #3
avatar+402 
+1

Oh right, thanks for correcting me geno! I missed out on that small detail!

jfan17  Mar 22, 2020

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