What is the f(x)=(sec(x)+tan(x))/(sec(x)-tan(x)) ?

The f(x)=(sec(x)+tan(x))/(sec(x)-tan(x)) is

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

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

Period : 2 π

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

Y Intercepts : (0, 1)

Asymptotes : Vertical x = \frac{π}{2} + 2 πn

Inflection Points : None

Interval Notation

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

Solution steps

Periodicity of

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

Domain of

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

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

Vertical

: x = \frac{π}{2} + 2 πn

Inflection Points of

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

None

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What is the f(x)=(sec(x)+tan(x))/(sec(x)-tan(x)) ?
The f(x)=(sec(x)+tan(x))/(sec(x)-tan(x)) is