let f: R  --->   R+ and  g: --> R+ . R be defined as     f(x) = ex       and g(x) = lnx.let f: R  ------>   R+      and       g: -------->...

let f: R  --->   R+ and  g: --> R+ . R be defined as     f(x) = ex       and g(x) = lnx.

let f: R  ------>   R+      and       g: --------> R+                   R be defined as            f(x) = ex       and g(x) = lnx.

Show that f and g are inverse of each other.

 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to follow the steps of procedure of finding the inverse of a function such that:

You need to substitute y for f(x) such that:

`y = e^x`

You need to substitute y for x and x for y such that:

`x = e^y`

You need to solve for y the equation x = e^y, hence you should take logarithms both sides such that:

`x = e^y`

`ln x = ln (e^y)`

You need to use power property of logarithms such that:

`ln x = y*ln e`

You need to remember that `ln e = 1`  such that:

`ln x = y`

Notice that the last line represents the function g(x) = ln x, hence, the function g(x) expresses the inverse of function f(x).

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