Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Find the domain and range of tan1x by plotting the graph.

Answer
VerifiedVerified
498.3k+ views
like imagedislike image
Hint: In the simplest form domain is all the values that go into the function and range is all the functions that come out of it.

Complete step-by-step answer:
Let us define the domain and range of
y =tan x
The domain of the function y =tan x is
 x(π2,π2)
 The range of the function y =tan x is
 y(,+)
 The function y=tan1x is symmetric to the function y=tan x with respect the line y=x
 Therefore, the domain is x(,+)
 and the range is y(π2,π2)
 Now we can draw the graph of the function from the observation and discuss it.
 
seo images



This the graph for the y=tan1x function.
Since the inverse function is obtained by reflecting the graph about the line y=x ,
The vertical asymptotes of the tangent function become horizontal asymptotes of the inverse tangent function.
As θ approaches ,tan1θ approaches π2asθθ,tan1θπ2
And by reflecting the function we get the graph of the function.


Note: In the first step students need to take this assumption y= tan x otherwise they would not be able to solve the problem. Also the students need to clearly understand the meaning of domain and range of a function to solve the problem.