What is the domain of y=sec(1/2 x) ?

The domain of y=sec(1/2 x) is 4pin<= x<pi+4pin\lor pi+4pin<x<3pi+4pin\lor 3pi+4pin<x<4pi+4pin

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domain of y=sec(1/2 x)

domain

y = sec (\frac{1}{2} x)

4 πn \leq x < π + 4 πn or π + 4 πn < x < 3 π + 4 πn or 3 π + 4 πn < x < 4 π + 4 πn

Interval Notation

Solution steps

Take the denominator(s) of

sec (\frac{1}{2} x)

and compare to zero:

x = π + 4 πn, x = 3 π + 4 πn

Periodicity of

sec (\frac{1}{2} x) : 4 π

Combine period:

4 πn \leq x < 4 π + 4 πn

and undefined points.

The domain is

4 πn \leq x < π + 4 πn or π + 4 πn < x < 3 π + 4 πn or 3 π + 4 πn < x < 4 π + 4 πn

e^{- l n (x)}

20 - x

y + x = - 4 x + (x - 2)^{2}

f (x) = x^{4} + \frac{4}{3 x ^{3}}

f (t) = cos (2 t)

What is the domain of y=sec(1/2 x) ?
The domain of y=sec(1/2 x) is 4pin<= x<pi+4pin\lor pi+4pin<x<3pi+4pin\lor 3pi+4pin<x<4pi+4pin