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

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

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

domain

f (x) = tan (\frac{1}{2} x + π) + 1

2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Interval Notation

[2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Solution steps

Take the denominator(s) of

tan (\frac{1}{2} x + π) + 1

and compare to zero:

x = π + 2 πn

Periodicity of

tan (\frac{1}{2} x + π) + 1 : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

f (x) = e^{5 x}

f (x) = 7 x + 9

f (x) = \frac{x ^{7} - 4 x ^{6} - 16 x ^{5} + 64 x ^{4}}{x}

f (x) = lo g_{10} (2 - x) + x - 3

g (x) = ln (x + 3)

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