What is the domain of f(x)=csc((2pi)/5 x)-3 ?

The domain of f(x)=csc((2pi)/5 x)-3 is 5n<x< 5/2+5n\lor 5/2+5n<x<5+5n

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domain of f(x)=csc((2pi)/5 x)-3

domain

f (x) = csc (\frac{2 π}{5} x) - 3

5 n < x < \frac{5}{2} + 5 n or \frac{5}{2} + 5 n < x < 5 + 5 n

Interval Notation

(5 n, \frac{5}{2} + 5 n) \cup (\frac{5}{2} + 5 n, 5 + 5 n)

Solution steps

Take the denominator(s) of

csc (\frac{2 π}{5} x) - 3

and compare to zero:

x = 5 n, x = \frac{5}{2} + 5 n

Periodicity of

csc (\frac{2 π}{5} x) - 3 : 5

Combine period:

5 n \leq x < 5 + 5 n

and undefined points.

The domain is

5 n < x < \frac{5}{2} + 5 n or \frac{5}{2} + 5 n < x < 5 + 5 n

f (x) = \frac{1}{16} x^{4}

f (x) = 2 x - \frac{4}{3}

3^{- x}

ln (e^{x} - 1) - ln (2) - 1

f (x) = x^{4} - 6 x^{2}

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