Question about inverse functions

So, if you have f(x) and inverse of f(x), does inverse of f(x)=1/f(x)
So, pretty much, does
-1
f (x)=1/f(x)?

No. When you are talking about inverse functions, you are talking about functional inverses, not multiplicative inverses.

e^x and ln(x) are inverse functions
tan(x) and arctan(x) are inverse functions
√x and x² are inverse functions

The hallmark of a pair of inverse functions is:
If u(x) and v(x) are inverse functions then u(v(x)) = v(u(x)) = x

For example:
√(x²) = (√x)² = x
tan(arctan(x)) = arctan(tan(x)) = x
etc.

The inverse of a function is not the same as the multiplicative inverse of that function.

Let f‾¹(x) = inverse function and g(x) = multiplicative inverse function
Then f ( f‾¹(x) ) = f‾¹( f(x) ) = x
. and f(x) * g(x) = 1