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Question

# The function f(x)=tan x where xϵ(−π4,π4) is in nature and the value of f(x) when x increases.

A
continuous
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B
discontinuous
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C
increases
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D
decreases
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Solution

## The correct options are A continuous C increasesLet's try to draw the function in a graph. The tangent function is discontinuous at odd integral multipleso of π2. Here the domain is xϵ(−π4,π4) for which the function doesn't have any breaks. Hence, in the given interval the function tan x is continuous. Or we can say that the function is continuous at each and every point in its defined domain. Also by observation, the function's increasing nature can also be noted. In fact, tan x is increasing everywhere it's continuous. This will be evident when you learn about slopes and derivatives.

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