
Find the domain and range of by plotting the graph.
Answer
498.9k+ views
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
The range of the function y =tan x is
The function is symmetric to the function y=tan x with respect the line y=x
Therefore, the domain is
and the range is
Now we can draw the graph of the function from the observation and discuss it.
This the graph for the 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 approaches approaches
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.
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
The range of the function y =tan x is
The function
Therefore, the domain is
and the range is
Now we can draw the graph of the function from the observation and discuss it.

This the graph for the
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
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.
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