What is the domain of csc(((x*pi))/2)+1 ?

The domain of csc(((x*pi))/2)+1 is 4n<x<2+4n\lor 2+4n<x<4+4n

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domain of csc(((x*pi))/2)+1

domain

csc (\frac{( x \cdot π )}{2}) + 1

4 n < x < 2 + 4 n or 2 + 4 n < x < 4 + 4 n

Interval Notation

(4 n, 2 + 4 n) \cup (2 + 4 n, 4 + 4 n)

Solution steps

Take the denominator(s) of

csc (\frac{x \cdot π}{2}) + 1

and compare to zero:

x = 4 n, x = 2 + 4 n

Periodicity of

csc (\frac{x \cdot π}{2}) + 1 : 4

Combine period:

4 n \leq x < 4 + 4 n

and undefined points.

The domain is

4 n < x < 2 + 4 n or 2 + 4 n < x < 4 + 4 n

f (x) = \frac{- 5 x - 10}{x ^{2} + 2 x}

\frac{x - 5}{x ^{2} - 25}

f (x) = 19 - 2 x

f (x) = 2 x^{2} - 5 x + 3

m = - \frac{1}{2}, (8, - 12)

What is the domain of csc(((x*pi))/2)+1 ?
The domain of csc(((x*pi))/2)+1 is 4n<x<2+4n\lor 2+4n<x<4+4n