Question

Which of the following is correct for a real function?

• A. Range of a real function should be subset of $R$
• B. If $f:R\to R$ and $f\left(x\right)=x^3-2|x|$, then it is real function
• C. If $f:R\to R$ and $f\left(x\right)=1-x^2$, then it is real function
• D. Domain of a real function should be subset of $R$

Answer 1

Answer: (A), (B), (C), (D)

Domain of a real function should be subset of $R$

A real function is a function whose preimage as well as image both are the subsets of real numbers $\left(R\right)$
i.e. for real functions,
Domain $\subseteq R$
and Range $\subseteq R$

$f\left(x\right)=1-x^2$
This function is defined for every real $x$ and for every real $x$, the image is always a real number.
So, it is a real function.

$f\left(x\right)=x^3-2|x|$
This function is defined for every real $x$ and for every real $x$, the image is always a real number.
So, it is a real function.