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Mark (√) against the correct answer in the following:

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.