The function f : R → R defined by $f(x)=e^x$ is __________.

one-one

Function f : R → R defined by $f(x)=e^x$.

Let $x_1,x_2∈R$ and $f(x_1)=f(x_2)$ or $e^{x_1}=e^{x_2}$ or $x_1=x_2$.

Therefore, f is one-one

Let $f(x)=e^x=y$.

Taking log on both sides, we get : x = log y.

We know that negative real numbers have no pre-image or the function is not onto and zero is not the image of any real numbers.

Therefore, function f is into.