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.