Which function is its own inverse? Please find three such functions and prove your finding algebraically.?

Answer 1

dy/dx = y
dy/y = dx
ln y = x + C
y = Ce^x ... this is the exponential function with coefficients...

substitute any real number for C(preferably not 0 cause its trivial)

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Answer 2

The inverse of a function f(x) is a function g(x) such that f(g(x)) = x and g(f(x)) = x.

Two obvious choices are f(x) = x and f(x) = -x. For example with f(x) = x, we have f(g(x)) = g(x) =x and g(f(x) = g(x) = x.

Note: The inverse of f(x) = e^x is g(x) = ln (x). Thus, e^x is not its own inverse.