What is the domain of f(x)=tan(2x+1) ?

The domain of f(x)=tan(2x+1) is pi/2 n<= x<-1/2+pi/4+pi/2 n\lor (-2+pi)/4+pi/2 n<x< pi/2+pi/2 n

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domain of f(x)=tan(2x+1)

domain

f (x) = tan (2 x + 1)

\frac{π}{2} n \leq x < - \frac{1}{2} + \frac{π}{4} + \frac{π}{2} n or \frac{- 2 + π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Interval Notation

[\frac{π}{2} n, - \frac{1}{2} + \frac{π}{4} + \frac{π}{2} n) \cup (\frac{- 2 + π}{4} + \frac{π}{2} n, \frac{π}{2} + \frac{π}{2} n)

Solution steps

Take the denominator(s) of

tan (2 x + 1)

and compare to zero:

x = - \frac{1}{2} + \frac{π}{4} + \frac{π}{2} n, x = \frac{- 2 + π}{4} + \frac{π}{2} n

Periodicity of

tan (2 x + 1) : \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{1}{2} + \frac{π}{4} + \frac{π}{2} n or \frac{- 2 + π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

g (x) = 3^{x} - 3

(x - 2) \cdot (3 x^{2} + 5 x)

x + 25

f (x) = \frac{3 x ^{2}}{4 x ^{2} - 3}

What is the domain of f(x)=tan(2x+1) ?
The domain of f(x)=tan(2x+1) is pi/2 n<= x<-1/2+pi/4+pi/2 n\lor (-2+pi)/4+pi/2 n<x< pi/2+pi/2 n