`f(x) = sqrt(1-sin(x))`

Domain of f(x) -->

Domain of sin(x) is all the Real numbers, `x in R` . For all the real numbers, sine would be in the following range,

`-1lt=sin(x)lt=+1`

Therefore, multiplying by -1,

`+1=gt-sin(x)=gt-1`

Adding +1,

`1+1=gt1-sin(x)=gt1-1`

Therefore,

`2=gt1-sin(x)=gt0`

We know for all real numbers `1- sin(x)` will be positive.

Therefore the expression inside the squareroot is always positive for all `x in R` . ** Therefore the Domain...**

(The entire section contains 264 words.)

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