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Popular >

f(x)=5-3csc(x)

Solution

f (x) = 5 - 3 csc (x)

Solution

Period : 2 π

Domain : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq 2 or f (x) \geq 8

X Intercepts : (arccsc (\frac{5}{3}) + 2 πn, 0), (π - arccsc (\frac{5}{3}) + 2 πn, 0)

Asymptotes : Vertical x = 2 πn, x = π + 2 πn

Extreme Points : Maximum (\frac{π}{2} + 2 πn, 2), Minimum (\frac{3 π}{2} + 2 πn, 8)

+1

Interval Notation

Domain : (2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Range : (- \infty, 2] \cup [8, \infty)

Solution steps

Periodicity of

5 - 3 csc (x) : 2 π

Domain of

5 - 3 csc (x) : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

5 - 3 csc (x) : f (x) \leq 2 or f (x) \geq 8

Axis interception points of

5 - 3 csc (x) :

X Intercepts

: (arccsc (\frac{5}{3}) + 2 πn, 0), (π - arccsc (\frac{5}{3}) + 2 πn, 0)

Asymptotes of

5 - 3 csc (x) :

Vertical

: x = 2 πn, x = π + 2 πn

Extreme Points of

5 - 3 csc (x) :

Maximum

(\frac{π}{2} + 2 πn, 2),

Minimum

(\frac{3 π}{2} + 2 πn, 8)

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Frequently Asked Questions (FAQ)

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