Mark (√) against the correct answer in the following

Question:

Mark (√) against the correct answer in the following

$f: C \rightarrow R: f(z)=|z|$ is

A. one - one and into

B. one - one and onto

C. many - one and into

D. many - one and onto

 

Solution:

Here in this range the lines cut the curve in 2 equal valued points of $y$ therefore the function $f(z)=|z|$ is not one - one

$\Rightarrow f(z)=$ many one

Range of $f(z)=[0, \infty) \neq R$ (codomain)

$\therefore f(z)$ is not onto.

$\Rightarrow f(z)=$ into

Hence, $f(z)=|z|$ is many one and into

 

 

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