Question:
Mark (√) against the correct answer in the following:
$f: R \rightarrow R: f(x)=x^{2}$ is
A. one - one and onto
B. one - one and into
C. many - one and onto
D. many - one and into
Solution:
$f(x)=x^{2}$
$\Rightarrow y=x^{2}$
in this range the lines cut the curve in 2 equal valued points of $y$, therefore, the function $f(x)=x^{2}$ is many one.
Range of $f(x)=(0, \infty) \neq R$ (codomain)
$\therefore f(x)$ is into
$\therefore f: R \rightarrow R: f(x)=x^{2}$ is many - one into
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