Answer:
(-π/2, π/2).
Step-by-step explanation:
The value of tan π/2 and tan (-π/2) s undefined so the domain is restricted to
(-π/2, π/2).
The domain of f(x)= tanx is restricted to ( -π/2, π/2) so that the inverse of the function exists. This means all the functional value of f(x) = [tex]tan^{-1}x[/tex] are on the interval (-π/2, π/2).
" The domain is the set of all the values which we input in the given variable of the function."
" Inverse of the trigonometric function where domain and range get interchange compare to trigonometric function."
According to the question,
Domain of the function f(x) = tanx is restricted to (-π/2, π/2) to make the function one -one, so that its inverse exists.
Hence the domain of f(x)= tanx is restricted to ( -π/2, π/2) so that the inverse of the function exists. This means all the functional value of f(x) = [tex]tan^{-1}x[/tex] are on the interval (-π/2, π/2).
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