Question:
Mark (√) against the correct answer in the following:
$f: R \rightarrow R: f(x)=x^{3}$ is
A. one - one and onto
B. one - one and into
C. many - one and onto
D. many - one and into
Solution:
$f(x)=x^{3}$
Since the function $f(x)$ is monotonically increasing from the domain $R \rightarrow R$
$\therefore f(x)$ is one -one
Range of $f(x)=(-\infty, \infty) \neq R$ (codomain)
$\therefore f(x)$ is into
$\therefore f: R \rightarrow R: f(x)=x^{3}$ is one - one into.
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