What is the domain of F(x)= 4/(sin(x))+2 ?

The domain of F(x)= 4/(sin(x))+2 is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of F(x)= 4/(sin(x))+2

domain

F (x) = \frac{4}{sin ( x )} + 2

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

\frac{4}{sin ( x )} + 2

and compare to zero:

x = 2 πn, x = π + 2 πn

Periodicity of

\frac{4}{sin ( x )} + 2 : 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

f (x) = 1 - [x]

y = \frac{x ^{2} - x - 6}{x ^{2} + 3 x + 2}

- \frac{1}{x - 6}

f (x) = \frac{5 x}{x + 9}

f (x) = 20 x - 33

What is the domain of F(x)= 4/(sin(x))+2 ?
The domain of F(x)= 4/(sin(x))+2 is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin