What is the domain of f(x)=5cot(x/2+pi/4) ?

The domain of f(x)=5cot(x/2+pi/4) is 2pin<= x<(3pi)/2+2pin\lor 2pi-pi/2+2pin<x<2pi+2pin

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domain of f(x)=5cot(x/2+pi/4)

domain

f (x) = 5 cot (\frac{x}{2} + \frac{π}{4})

2 πn \leq x < \frac{3 π}{2} + 2 πn or 2 π - \frac{π}{2} + 2 πn < x < 2 π + 2 πn

Interval Notation

[2 πn, \frac{3 π}{2} + 2 πn) \cup (2 π - \frac{π}{2} + 2 πn, 2 π + 2 πn)

Solution steps

Take the denominator(s) of

5 cot (\frac{x}{2} + \frac{π}{4})

and compare to zero:

x = \frac{3 π}{2} + 2 πn, x = 2 π - \frac{π}{2} + 2 πn

Periodicity of

5 cot (\frac{x}{2} + \frac{π}{4}) : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq x < \frac{3 π}{2} + 2 πn or 2 π - \frac{π}{2} + 2 πn < x < 2 π + 2 πn

y = \frac{2 x ^{2}}{1 - x ^{2}}

f (x) = sin (x) + cos (x)

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

f (x) = \frac{25 - x ^{2}}{x ^{2} - 16}

f (x) = \frac{2 x}{36 - x}

What is the domain of f(x)=5cot(x/2+pi/4) ?
The domain of f(x)=5cot(x/2+pi/4) is 2pin<= x<(3pi)/2+2pin\lor 2pi-pi/2+2pin<x<2pi+2pin