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

The domain of f(x)=2+tan(x) is pin<= x< pi/2+pin\lor pi/2+pin<x<pi+pin

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

domain

f (x) = 2 + tan (x)

πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Interval Notation

[πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Solution steps

Take the denominator(s) of

2 + tan (x)

and compare to zero:

x = \frac{π}{2} + πn

Periodicity of

2 + tan (x) : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

f (x) = \frac{x}{x ^{2} + 13 x + 40}

\frac{1}{x ^{2} - 4}

f (x) = (x - 8)^{\frac{1}{2}}

\frac{6 x - 5}{x + 9}

(- 5, 5), (2, 2)

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