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Popular >

f(x)=csc(2x)-1

Solution

f (x) = csc (2 x) - 1

Solution

Period : π

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

Range : f (x) \leq - 2 or f (x) \geq 0

X Intercepts : (\frac{π}{4} + πn, 0)

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

Extreme Points : Minimum (\frac{π}{4} + πn, 0), Maximum (\frac{3 π}{4} + πn, - 2)

+1

Interval Notation

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

Range : (- \infty, - 2] \cup [0, \infty)

Solution steps

Periodicity of

csc (2 x) - 1 : π

Domain of

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

Range of

csc (2 x) - 1 : f (x) \leq - 2 or f (x) \geq 0

Axis interception points of

csc (2 x) - 1 :

X Intercepts

: (\frac{π}{4} + πn, 0)

Asymptotes of

csc (2 x) - 1 :

Vertical

: x = \frac{π}{2} + πn, x = πn

Extreme Points of

csc (2 x) - 1 :

Minimum

(\frac{π}{4} + πn, 0),

Maximum

(\frac{3 π}{4} + πn, - 2)

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