Curve study/e to the power -1 over x/Exercise

We consider the function

$f\colon \mathbb {R} \setminus \{0\}\longrightarrow \mathbb {R} ,x\longmapsto f(x)=e^{-{\frac {1}{x}}}.$

a) Investigate the monotony behavior of this function.

b) Prove that this function is injective.

c) Determine the image of ${}f$.

d) Determine the inverse function on the image for this function.

e) Sketch the graph of the function ${}f$.

Create a solution