What is the domain of y=csc((pix)/2)+1 ?

The domain of y=csc((pix)/2)+1 is 4n<x<2+4n\lor 2+4n<x<4+4n

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domain of y=csc((pix)/2)+1

domain

y = csc (\frac{π x}{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{π x}{2}) + 1

and compare to zero:

x = 4 n, x = 2 + 4 n

Periodicity of

csc (\frac{π x}{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

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