Inequality between two functions I have a two functions defined for $x > 1$, and $c \in (0,1)$:
$$
f(x) = 1-\exp\left(-\frac{c}{x^2} \right),
$$
and
$$
g(x) = \exp\left(-\frac{x}{c} \right).
$$
From graphical tool (
https://www.desmos.com/calculator/hr8n8kkpym ), I know $f(x) > g(x)$. How can I prove this inequality analytically? 

As x tends to infinity f(x) tends to 0 in a slower rate which can be seen by differentiation compared to g(x) 
You can prove it by finding inverse function of f and g which are simpler to prove than this
