What is the domain of tan(3x-5) ?

The domain of tan(3x-5) is pi/3 n<= x<(10-3pi)/6+pi/3 n\lor (10-3pi)/6+pi/3 n<x< pi/3+pi/3 n

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domain of tan(3x-5)

domain

tan (3 x - 5)

\frac{π}{3} n \leq x < \frac{10 - 3 π}{6} + \frac{π}{3} n or \frac{10 - 3 π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

Interval Notation

[\frac{π}{3} n, \frac{10 - 3 π}{6} + \frac{π}{3} n) \cup (\frac{10 - 3 π}{6} + \frac{π}{3} n, \frac{π}{3} + \frac{π}{3} n)

Solution steps

Take the denominator(s) of

tan (3 x - 5)

and compare to zero:

x = \frac{10 - 3 π}{6} + \frac{π}{3} n

Periodicity of

tan (3 x - 5) : \frac{π}{3}

Combine period:

\frac{π}{3} n \leq x < \frac{π}{3} + \frac{π}{3} n

and undefined points.

The domain is

\frac{π}{3} n \leq x < \frac{10 - 3 π}{6} + \frac{π}{3} n or \frac{10 - 3 π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

f (x) = \frac{1}{∣ x ∣ - x}

f (x) = \frac{2 - x}{lo g _{10} ( x )}

f (x) = 8 x - 1704

f (x) = 4 x - 6, x \geq - 2

f (x) = - \frac{1}{4} x^{3} - 13 x^{2} + 3 x - 9

What is the domain of tan(3x-5) ?
The domain of tan(3x-5) is pi/3 n<= x<(10-3pi)/6+pi/3 n\lor (10-3pi)/6+pi/3 n<x< pi/3+pi/3 n