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Are exponential functions necessarily one to one?

1 Answer

Dec 1, 2015

If #a, b in RR# and #a, b > 0#, then #f(x) = ab^x# is one-one from #RR# onto #(0, oo)#

Apart from such normal cases, exponential functions are often not one-one.

Explanation:

As a Complex valued function from #CC->CC# \ #{ 0 }#, the exponential function #exp(z) = e^z# is many to one.

For example, #e^(2k pi i) = 1# for all #k in ZZ#

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