What is the domain of f(x)=2csc(4x)-3 ?

The domain of f(x)=2csc(4x)-3 is pi/2 n<x< pi/4+pi/2 n\lor pi/4+pi/2 n<x< pi/2+pi/2 n

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domain of f(x)=2csc(4x)-3

domain

f (x) = 2 csc (4 x) - 3

\frac{π}{2} n < x < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Interval Notation

(\frac{π}{2} n, \frac{π}{4} + \frac{π}{2} n) \cup (\frac{π}{4} + \frac{π}{2} n, \frac{π}{2} + \frac{π}{2} n)

Solution steps

Take the denominator(s) of

2 csc (4 x) - 3

and compare to zero:

x = \frac{π}{2} n, x = \frac{π}{4} + \frac{π}{2} n

Periodicity of

2 csc (4 x) - 3 : \frac{π}{2}

Combine period:

\frac{π}{2} n \leq x < \frac{π}{2} + \frac{π}{2} n

and undefined points.

The domain is

\frac{π}{2} n < x < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

f (x) = x \cdot ln (x)

3^{x} + 3

\frac{x - 5}{3 x - 6}

f (x) = 9 x^{2} + 6 x

f (x) = - 2^{5 - x} + 4

What is the domain of f(x)=2csc(4x)-3 ?
The domain of f(x)=2csc(4x)-3 is pi/2 n<x< pi/4+pi/2 n\lor pi/4+pi/2 n<x< pi/2+pi/2 n