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

The correct option is A many – one and into

Since, f (x + iy) = f (x - iy) $\therefore$ f is many – one
Also, Range $=R^{+}$ and codomain = R.
$\therefore$ Range $⊏$ codomain $\Rightarrow$ f is into.
Hence, f is many – one into.