What is the domain of tan(pix) ?

The domain of tan(pix) is 1<= x< 1/2+1\lor 1/2+1<x<1+1

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domain of tan(pix)

domain

tan (π x)

1 \leq x < \frac{1}{2} + 1 or \frac{1}{2} + 1 < x < 1 + 1

Interval Notation

[1, \frac{1}{2} + 1) \cup (\frac{1}{2} + 1, 1 + 1)

Solution steps

Take the denominator(s) of

tan (π x)

and compare to zero:

x = \frac{1}{2} + 1 \cdot n

Periodicity of

tan (π x) : 1

Combine period:

1 \leq x < 1 + 1

and undefined points.

The domain is

1 \leq x < \frac{1}{2} + 1 or \frac{1}{2} + 1 < x < 1 + 1

What is the domain of tan(pix) ?
The domain of tan(pix) is 1<= x< 1/2+1\lor 1/2+1<x<1+1