Question

The function $f\left(x\right)=tanxwherexϵ(\frac{-\pi }{4},\frac{\pi }{4})$ is in nature and the value of $f\left(x\right)$ when x increases.

• A. continuous
• B. discontinuous
• C. increases
• D. decreases

Answer 1

Answer: (A), (C)

The correct options are
A continuous
C increases

Let's try to draw the function in a graph.

The tangent function is discontinuous at odd integral multipleso of $\frac{\pi }{2}$. Here the domain is $xϵ(\frac{-\pi }{4},\frac{\pi }{4})$ 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.