We are asked to determine if the function 
has an inverse function by finding if the function is strictly monotonic on its entire domain using the derivative. The domain is all reals.
and 
for all real x so the function is strictly monotonic (in this case strictly increasing) on its entire domain and thus has an inverse function.
The graph:
We are asked to determine if the function has an inverse function by finding if the function is strictly monotonic on its entire domain using the derivative. The domain is all reals.
and for all real x so the function is strictly monotonic (in this case strictly increasing) on its entire domain and thus has an inverse function.
The graph:
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