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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