Question

Define what is meant by a real valued fuction?

Answer 1

A real-valued function f is one whose codomain is the set of real numbers or a subset thereof.
This includes integers, fractions, irrational numbers, and transcendental numbers

Sometime this symbol is used to denote the real numbers.
\[\mathbb{R} \]

This does not include complex numbers, numbers consisting of a real and imaginary part.
So,
\[ y = sin(x), y \in \mathbb{R}\]
but,
\[y = isin(x), y \in \mathbb{C}\]

Answer 2

put it simply that range of real valued function is only real numbers, and not complex i.e y=x^2+x+1 ....is not a real valued function ,

Answer 3

but this equation gives real numbers always .could you just GIVE A CASE WHERE THE EQUATION DOES NOT GIVE A REAL NUMBER IF I WAS TO SUBSTITUTE FOR ANY VALUE FROM THE NUMBER LINE