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

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

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domain of f(x)=sqrt(sin(x)+1/2)

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

The function domain

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

y = sin (e^{- t})

f (x) = \frac{1}{x - 81}

f (x) = 2 x^{3} - 6 x^{2} + 4

f (x) = 4 x^{2} - 12 x + 8

2 t

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