f : R × R → R such that f(x + iy) = √ x 2 + y 2 . Then, f is Options: A . &nbsp many – one and into B . &nbsp one-one and onto C . &nbsp many – one and onto D . &nbsp one – one and into

f:R×R→R such that f(x + iy) = √x2+y2. Then, f is

Question -

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

Options:

A . many – one and into

B . one-one and onto

C . many – one and onto

D . one – one and into

Answer: Option A
:
A
Since, f (x + iy) = f (x - iy)

∴

f is many – one
Also, Range

= R^{+}

and codomain = R.

∴

Range

⊏

codomain

\Rightarrow

f is into.
Hence, f is many – one into.

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