Are exponential functions one to one?

Exponential functions are one-to-one functions. • graph crosses the y-axis at (0,1). • when b > 1, the graph increases. • when 0 < b < 1, the graph decreases. • the domain is all real numbers. • the range is all positive real numbers (never zero). • graph passes the vertical line test for functions. read more

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. read more

After learning the definition of a function, we can extend it to define a one to one function. A one to one function has not only one output for every input, but also only one input in the domain for every output in therange. Another interesting type is an invertible function, or a function that has an inverse. read more