What is the domain of tan(x-pi/2) ?

The domain of tan(x-pi/2) is pin<x<pi+pin

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domain of tan(x-pi/2)

domain

tan (x - \frac{π}{2})

πn < x < π + πn

Interval Notation

(πn, π + πn)

Solution steps

Take the denominator(s) of

tan (x - \frac{π}{2})

and compare to zero:

x = πn

Periodicity of

tan (x - \frac{π}{2}) : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn < x < π + πn

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

lo g_{10} (x^{2})

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

\frac{1}{x + 10}

f (x) = x + 4 + 1 - x