What is the domain of f(x)=-0.5sec(pi/2 x+pi/3) ?

The domain of f(x)=-0.5sec(pi/2 x+pi/3) is 4n<= x< 1/3+4n\lor 1/3+4n<x< 7/3+4n\lor 7/3+4n<x<4+4n

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domain of f(x)=-0.5sec(pi/2 x+pi/3)

domain

f (x) = - 0.5 sec (\frac{π}{2} x + \frac{π}{3})

4 n \leq x < \frac{1}{3} + 4 n or \frac{1}{3} + 4 n < x < \frac{7}{3} + 4 n or \frac{7}{3} + 4 n < x < 4 + 4 n

Interval Notation

Solution steps

Take the denominator(s) of

- 0.5 sec (\frac{π}{2} x + \frac{π}{3})

and compare to zero:

x = \frac{1}{3} + 4 n, x = \frac{7}{3} + 4 n

Periodicity of

- 0.5 sec (\frac{π}{2} x + \frac{π}{3}) : 4

Combine period:

4 n \leq x < 4 + 4 n

and undefined points.

The domain is

4 n \leq x < \frac{1}{3} + 4 n or \frac{1}{3} + 4 n < x < \frac{7}{3} + 4 n or \frac{7}{3} + 4 n < x < 4 + 4 n

f (x) = \frac{x ^{2} - 1}{x ^{2} - x}

x + 5 + 2

x + 5 + 4

\frac{( 7 x + 18 )}{x ^{2} - x - 4}

2 tan (x)

What is the domain of f(x)=-0.5sec(pi/2 x+pi/3) ?
The domain of f(x)=-0.5sec(pi/2 x+pi/3) is 4n<= x< 1/3+4n\lor 1/3+4n<x< 7/3+4n\lor 7/3+4n<x<4+4n