A function f:R→R𝑓:𝑅→𝑅 defined by f(x)=x−−√𝑓(𝑥)=𝑥 is a real valued function.

The function f(x) = √x is indeed a real-valued function. This means that for every real number x in the domain, the output f(x) is also a real number.

Here's a step-by-step explanation:

1. The domain of the function f(x) = √x is all non-negative real numbers. This is because we cannot take the square root of a negative number in the real number system.

2. The range of the function f(x) = √x is also all non-negative real numbers. This is because the square root of any real number is always non-negative.

3. Therefore, for every real number x in the domain, the output f(x) is also a real number. Hence, f(x) = √x is a real-valued function.