Question

What is the inverse of the function??

Answer 1

`\(\begin{matrix} y=ln(x+3)\\ e^y=x+3\\ e^y-3=x\\ swap ~x~and~y\\ \huge\underline{y=e^x-3}} \end{matrix}\)`

To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:

- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).

- Swap x and f(x).

- The result is the inverse of the original function
`f^(-1)(x)`.

-------------------------

Apply that on your function

`\(\begin{matrix} y=ln(x+3)\\ e^y=x+3\\ e^y-3=x\\ swap ~x~and~y\\ \huge\underline{y=e^x-3}} \end{matrix}\)`