What is the domain of f(x)=sqrt(1-4cos(x)) ?

The domain of f(x)=sqrt(1-4cos(x)) is arccos(1/4)+2pin<= x<= 2pi-arccos(1/4)+2pin

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domain of f(x)=sqrt(1-4cos(x))

domain

f (x) = 1 - 4 cos (x)

arccos (\frac{1}{4}) + 2 πn \leq x \leq 2 π - arccos (\frac{1}{4}) + 2 πn

Interval Notation

[arccos (\frac{1}{4}) + 2 πn, 2 π - arccos (\frac{1}{4}) + 2 πn]

Solution steps

Find non-negative values for radicals:

arccos (\frac{1}{4}) + 2 πn \leq x \leq 2 π - arccos (\frac{1}{4}) + 2 πn

The function domain

arccos (\frac{1}{4}) + 2 πn \leq x \leq 2 π - arccos (\frac{1}{4}) + 2 πn

f (x) = 3 x^{2} + 15 x + 18

- 3 tan (3 x + π)

\frac{x + 4}{x ^{2} + x - 3}

f (x) = 3 x^{2} + 15 x + 10

f (x) = \frac{2 x - 3}{x + 1}

What is the domain of f(x)=sqrt(1-4cos(x)) ?
The domain of f(x)=sqrt(1-4cos(x)) is arccos(1/4)+2pin<= x<= 2pi-arccos(1/4)+2pin