What is the domain of f(x)= 3/(sin(x))+5 ?

The domain of f(x)= 3/(sin(x))+5 is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of f(x)= 3/(sin(x))+5

domain

f (x) = \frac{3}{sin ( x )} + 5

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{3}{sin ( x )} + 5

and compare to zero:

x = 2 πn, x = π + 2 πn

Periodicity of

\frac{3}{sin ( x )} + 5 : 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

g (x) = \frac{4 + x}{1 - x}

f (x) = \frac{1}{x ^{2} + 25}

4 + x - 2

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

f (x) = \frac{2}{( x ^{2} - 4 )}

What is the domain of f(x)= 3/(sin(x))+5 ?
The domain of f(x)= 3/(sin(x))+5 is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin