Question

If the domain of the function $f$ is $R$, then which of the following will not be a real valued function ?

• A. $f\left(x\right)=x^2$
• B. $f\left(x\right)=|x-2|$
• C. $f\left(x\right)=5x-7$
• D. $f\left(x\right)=\sqrt{x}$

Answer 1

The correct option is D $f\left(x\right)=\sqrt{x}$

For real valued function, the output obtained from the function should be a real number.
For $f\left(x\right)=x^2$
For every real input this function always gives real output.
It is a real valued function.

For $f\left(x\right)=|x-2|$
For every real input this function always gives real output.
It is a real valued function.

For $f\left(x\right)=5x-7$
For every real input this function always gives real output.
It is a real valued function.

For $f\left(x\right)=\sqrt{x}$
This function gives real output only when $x\in R^{+}$
When $x\in R^{-}$, it won't give real output.
So it is not a real valued function.