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

Question:

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

$f: R^{+} \rightarrow R^{+}: f(x)=e^{x}$ is

A. many - one and into

B. many - one and onto

C. one - one and into

D. one - one and onto

 

Solution:

$f(x)=e^{x}$

Since the function $f(x)$ is monotonically increasing from the domain $R^{+} \rightarrow R^{+}$

$\therefore f(x)$ is one -one

Range of $f(x)=(1, \infty)=R^{+}$(codomain)

$\therefore f(x)$ is onto

$\therefore f: R^{+} \rightarrow R^{+}: f(x)=e^{x}$ is one - one onto.

 

 

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