What is the domain of y=3tan(4x+6)-3 ?

The domain of y=3tan(4x+6)-3 is pi/4 n<= x<(-12+5pi)/8+pi/4 n\lor (-12+5pi)/8+pi/4 n<x< pi/4+pi/4 n

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domain of y=3tan(4x+6)-3

domain

y = 3 tan (4 x + 6) - 3

\frac{π}{4} n \leq x < \frac{- 12 + 5 π}{8} + \frac{π}{4} n or \frac{- 12 + 5 π}{8} + \frac{π}{4} n < x < \frac{π}{4} + \frac{π}{4} n

Interval Notation

[\frac{π}{4} n, \frac{- 12 + 5 π}{8} + \frac{π}{4} n) \cup (\frac{- 12 + 5 π}{8} + \frac{π}{4} n, \frac{π}{4} + \frac{π}{4} n)

Solution steps

Take the denominator(s) of

3 tan (4 x + 6) - 3

and compare to zero:

x = \frac{- 12 + 5 π}{8} + \frac{π}{4} n

Periodicity of

3 tan (4 x + 6) - 3 : \frac{π}{4}

Combine period:

\frac{π}{4} n \leq x < \frac{π}{4} + \frac{π}{4} n

and undefined points.

The domain is

\frac{π}{4} n \leq x < \frac{- 12 + 5 π}{8} + \frac{π}{4} n or \frac{- 12 + 5 π}{8} + \frac{π}{4} n < x < \frac{π}{4} + \frac{π}{4} n

\frac{75 p}{85 - p}

y = - \frac{7}{2} x + 2

x^{3} - 12 x + 1

f (x) = ln (x^{4} - 6)

f (x) = 3 x + 5

What is the domain of y=3tan(4x+6)-3 ?
The domain of y=3tan(4x+6)-3 is pi/4 n<= x<(-12+5pi)/8+pi/4 n\lor (-12+5pi)/8+pi/4 n<x< pi/4+pi/4 n