There are two common uses of the word inverse. In arithmetic, we may speak of the multiplicative inverse and in so doing, we may most often omit the word “multiplicative”. A multiplicative inverse is a number (or symbols representing a number) which will multiply some other number to yield the value $1$. If our number is $a$, then its multiplicative inverse is written as $a^{-1}$ and it is equal to $1/a$.
Another common use for “inverse” is in the context of an inverse function. These are also often written as $f^{-1}$, but they never mean $1/f$. An inverse function is one that reverts an image back to the input argument. As an example, $f(x)=sin^{-1}(x)$. Here, $f(x)$ is said to be the inverse sine. You probably know that we mean the $arcsin(x)$, which is a function and definitely not $1/sin(x)$. Another example is a polynomial. $$f(x)=3x+4$$ Then the inverse function, $$g(f(x))=\frac{f(x)-4}{3}.$$ A less formal way to write the same thing is $y=3x+4$ and $x=\frac{y-4}{3}$.
Yet another example; $f(x)=e^{x}$ and $g(f(x))=\log(e^{x})$. This last example might benefit from a numerical demonstration.
$$f(3)=e^{3}=20.09...$$ $$g(20.09...)=\log(20.09...)=3$$ Similarly, if $f(x)=\log(x)$, then $g(f(x))=e^{\log(x)}$. So the exponential function and the log function are inverses of each other.Just knowing the name of an inverse function will not normally explain how it is computed. The computation is likely to be a topic that must be addressed independently.