What is the domain of tan(2x-5) ?

The domain of tan(2x-5) is pi/2 n<= x<(10-3pi)/4+pi/2 n\lor (10-3pi)/4+pi/2 n<x< pi/2+pi/2 n

domain of tan(2x-5)

domain

tan (2 x - 5)

\frac{π}{2} n \leq x < \frac{10 - 3 π}{4} + \frac{π}{2} n or \frac{10 - 3 π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Interval Notation

Solution steps

Take the denominator(s) of

tan (2 x - 5)

and compare to zero:

x = \frac{10 - 3 π}{4} + \frac{π}{2} n

Periodicity of

tan (2 x - 5) : \frac{π}{2}

Combine period:

\frac{π}{2} n \leq x < \frac{π}{2} + \frac{π}{2} n

and undefined points.

The domain is

\frac{π}{2} n \leq x < \frac{10 - 3 π}{4} + \frac{π}{2} n or \frac{10 - 3 π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

f (x) = - sin (\frac{1}{2} x + \frac{5 π}{3})

f (x) = - x + 3 + 1

x^{2} + y^{2} - 2 x = 0

\frac{x ^{2} - 8}{x - 3}

\frac{6}{x} + 12

What is the domain of tan(2x-5) ?
The domain of tan(2x-5) is pi/2 n<= x<(10-3pi)/4+pi/2 n\lor (10-3pi)/4+pi/2 n<x< pi/2+pi/2 n