What is the domain of f(x)=sqrt(1-2sin(x)) ?

The domain of f(x)=sqrt(1-2sin(x)) is -(7pi)/6+2pin<= x<= pi/6+2pin

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domain of f(x)=sqrt(1-2sin(x))

domain

f (x) = 1 - 2 sin (x)

- \frac{7 π}{6} + 2 πn \leq x \leq \frac{π}{6} + 2 πn

Interval Notation

[- \frac{7 π}{6} + 2 πn, \frac{π}{6} + 2 πn]

Solution steps

Find non-negative values for radicals:

- \frac{7 π}{6} + 2 πn \leq x \leq \frac{π}{6} + 2 πn

The function domain

- \frac{7 π}{6} + 2 πn \leq x \leq \frac{π}{6} + 2 πn

What is the domain of f(x)=sqrt(1-2sin(x)) ?
The domain of f(x)=sqrt(1-2sin(x)) is -(7pi)/6+2pin<= x<= pi/6+2pin