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Popular Functions >

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

Solution

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

Solution

Period : π

Domain : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

X Intercepts : (\frac{π}{4} + πn, 0), Y Intercepts : (0, - 1)

Asymptotes : Vertical x = \frac{3 π}{4} + πn

Inflection Points : (\frac{π}{4} + πn, 0)

+1

Interval Notation

Domain : [πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, \frac{3 π}{4} + πn) \cup (\frac{3 π}{4} + πn, π + πn)

Solution steps

Periodicity of

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

Domain of

\frac{tan ( x ) - 1}{tan ( x ) + 1} : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

Axis interception points of

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

X Intercepts

: (\frac{π}{4} + πn, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

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

Vertical

: x = \frac{3 π}{4} + πn

Inflection Points of

\frac{tan ( x ) - 1}{tan ( x ) + 1} : (\frac{π}{4} + πn, 0)

Graph

Popular Examples

f(x)=-(1/3)^{x+2}

f(x)=arctan(x/5)

Frequently Asked Questions (FAQ)

What is the f(x)=(tan(x)-1)/(tan(x)+1) ?
The f(x)=(tan(x)-1)/(tan(x)+1) is