# How do you find the inverse of  y = e^x-1/x?

Oct 5, 2016

See below

#### Explanation:

To find the inverse of a given function, you need to isolate the $x$ variable.

For example, if you have $y = 2 x + 7$, you can do the following:

$y = 2 x + 7 \setminus \to y - 7 = 2 x \setminus \to x = \frac{y - 7}{2}$

In your case, it's not possible to isolate $x$, so you can't find an explicit expression for the inverse of your function.

The only thing you can do is something graphic, since the inverse of a function is obtained via symmetry with respect to the $y = x$ line.

So, you can draw the graph of ${e}^{x} - \frac{1}{x}$, and then mirror it, and it would be the graph of the inverse function.

Oct 6, 2016

As of now, there is no way of finding the inverse.

#### Explanation:

Unfortunately, the distributive law is not applicable for inversion.

This means that if # y=f(x) + g(x), x is not the sum of the inverses of

f(x) and g(x).,

For example, if f(x) =x, g(x)=2 and y = f(x) + g(x) = x + 2,

inversely x= y-2..

The sum of the separate inverses is y+1/2.

Here, f(x) = ${e}^{x} \mathmr{and} g \left(x\right) = - \frac{1}{x}$.

Despite that separate inverses are known as .ln y and -1/y,

we do not have a method to bring out the inverse of f+g.