Question

$f:R\times R\to R$ such that $f(x+iy)=+\sqrt{x^2+y^2}$.Then $f$ is

• A. many-one and into
• B. one-one and onto
• C. many-one and onto
• D. one-one and into

Answer 1

Answer: (A)

many-one and into

$f\left(z\right)=|z|$ where z is a complex number.

Now $f\left(x\right)\ge 0$

and $f\left(z\right)=f\left(\overline{z}\right)=|z|$

Hence $f\left(z\right)$ is a many one and into function.