Find the range of the function, `f(x) = 3 − e^x`.

Explanation

`y = 3 − e^x`
`implies e^x = 3 − y`
or, `x = ln(3 − y)`............(1)
Domain of above function (1) is `3 − y gt 0` or, `y lt 3`. This domain becomes range of the original function `f(x)`.
Note that `f(x)` is a bijective.
Note : This technique can be used even if function is not bijective, but case should be taken to include relevant values only.