What is the domain and range of f(x)=sqrt[cos[x]]

empalhaviyt

empalhaviyt

Answered question

2022-08-10

What is the domain and range of f ( x ) = cos [ x ] ?

Answer & Explanation

Bradley Forbes

Bradley Forbes

Beginner2022-08-11Added 12 answers

If author used square brackets inside cos just as brackets (not as an absolute value, which it looks like in a small font), than here is the explanation.
Also it should be noted that the square root in this problem used without ± sign implies arithmetic square root, that is only its non-negative value.
Square root requires cos x to be non-negative, which entails that xmust be in the intervals [ π 2 + 2 π n , π 2 + 2 π n ] for all integer n. That assures non-negativity of cos x and, therefore, constitutes the domain of this function.
In this domain cos x ranges in the interval [0,1] and square root of it also will be in the same range.

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