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Popular >

f(x)=(sec(x)-1)/(sec(x)+1)

Solution

f (x) = \frac{sec ( x ) - 1}{sec ( x ) + 1}

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range : 0 \leq f (x) < 1 or f (x) > 1

X Intercepts : (2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = π + 2 πn

Extreme Points : None

+1

Interval Notation

Domain : [2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, π + 2 πn) \cup (π + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Range : [0, 1) \cup (1, \infty)

Solution steps

Periodicity of

\frac{sec ( x ) - 1}{sec ( x ) + 1} : 2 π

Domain of

\frac{sec ( x ) - 1}{sec ( x ) + 1} : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

\frac{sec ( x ) - 1}{sec ( x ) + 1} : 0 \leq f (x) < 1 or f (x) > 1

Axis interception points of

\frac{sec ( x ) - 1}{sec ( x ) + 1} :

X Intercepts

: (2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{sec ( x ) - 1}{sec ( x ) + 1} :

Vertical

: x = π + 2 πn

Extreme Points of

\frac{sec ( x ) - 1}{sec ( x ) + 1} :

None

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Frequently Asked Questions (FAQ)

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