What is the domain of+(-3)csc(2pi+x) ?

The domain of+(-3)csc(2pi+x) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of+(-3)csc(2pi+x)

domain

+ (- 3) csc (2 π + x)

2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Interval Notation

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

Solution steps

Take the denominator(s) of

+ (- 3) csc (2 π + x)

and compare to zero:

x = 2 πn, x = π + 2 πn

Periodicity of

+ (- 3) csc (2 π + x) : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

\frac{- 2 x + 4}{x ^{2} - 9}

f (x) = 5 x - 3 f (x) = \frac{9 x ^{2} - 4}{3 x + 2}

f (x) = x^{2} + 4 x - 12

g (x) = \frac{x + 7}{x ^{2} - 49}

f (x) = lo g_{\frac{1}{4}} (x^{2} - 4 x + 4)

What is the domain of+(-3)csc(2pi+x) ?
The domain of+(-3)csc(2pi+x) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin