The function fx-tan x where x -4-4-

Let's try to draw the function in a graph. Here not that in the domain i.e. x=π2 is not present. Domain is x ∈( π4,π4) for which the function doesn't have an ...

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Standard XII

Mathematics

Graphical Interpretation of Continuity

The function ...

Question

The function $f (x) = tan x$ where $x \in (\frac{- π}{4}, \frac{π}{4})$ .

is continuous

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is discontinuous

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is increasing

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is decreasing

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Solution

The correct option is C
is increasing

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

Here not that in the domain i.e. $x = \frac{π}{2}$ is not present. Domain is $x \in (\frac{- π}{4}, \frac{π}{4})$ for which the function doesn't have any breaks.

Hence in the given interval the function $tan x$ is continuous or we can say the function is continuous at each and every point in its defined domain.

Also just observation, the function's increasing nature can also be noted.

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Similar questions

The function $f (x) = tan x$ where $x \in (\frac{- π}{4}, \frac{π}{4})$ .

Q. The function

f (x) = t a n x w h e r e x ϵ (\frac{- π}{4}, \frac{π}{4})

is in nature and the value of

f (x)

when x increases.

Q. Let

f (x) = \frac{1 - tan x}{4 x - π}, x \neq \frac{π}{4}

, then

lim x \to \frac{π}{4} f (x) =

Q. If the function

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \begin{matrix} {(1 - | tan x |)}^{a / | tan x |}, & - \frac{π}{4} < x < 0 \end{matrix} \begin{matrix} b, & x = 0 \end{matrix} \begin{matrix} e^{\frac{sin 3 x}{sin 2 x}}, & 0 < x < \frac{π}{4} \end{matrix} \end{matrix}

is continuous at

x = 0

, then

Q. In the interval

(- \frac{π}{4}, \frac{π}{4})

, the function

f (x) = t a n x

is .

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The function f(x)=tanx where x∈(−π4,π4).

The function $f (x) = tan x$ where $x \in (\frac{- π}{4}, \frac{π}{4})$ .