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Popular >

f(x)=(tan(x))/(tan^2(x)-1)

Solution

f (x) = \frac{tan ( x )}{tan ^{2} ( x ) - 1}

Solution

Period : \frac{π}{2}

Domain : \frac{π}{2} n < x < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Range : f (x) < 0 or f (x) > 0

X Intercepts : (\frac{πn}{2}, 0)

Asymptotes : Vertical x = \frac{π}{4} + \frac{π}{2} n

Extreme Points : None

+1

Interval Notation

Domain : (\frac{π}{2} n, \frac{π}{4} + \frac{π}{2} n) \cup (\frac{π}{4} + \frac{π}{2} n, \frac{π}{2} + \frac{π}{2} n)

Range : (- \infty, 0) \cup (0, \infty)

Solution steps

Periodicity of

\frac{tan ( x )}{tan ^{2} ( x ) - 1} : \frac{π}{2}

Domain of

\frac{tan ( x )}{tan ^{2} ( x ) - 1} : \frac{π}{2} n < x < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Range of

\frac{tan ( x )}{tan ^{2} ( x ) - 1} : f (x) < 0 or f (x) > 0

Axis interception points of

\frac{tan ( x )}{tan ^{2} ( x ) - 1} :

X Intercepts

: (\frac{πn}{2}, 0)

Asymptotes of

\frac{tan ( x )}{tan ^{2} ( x ) - 1} :

Vertical

: x = \frac{π}{4} + \frac{π}{2} n

Extreme Points of

\frac{tan ( x )}{tan ^{2} ( x ) - 1} :

None

Popular Examples

f (x) = 5 x^{\frac{4}{5}}

f (x) = 6 x^{2} - 7 x + 3

f (x) = 6 x^{2} - 7 x - 3

f (x) = 10 x - x

f = f^{9}

Frequently Asked Questions (FAQ)

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