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 $f^{-1}(x)$.

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Apply that on your function
$\(\begin{matrix} y=ln(x+3)\\ e^y=x+3\\ e^y-3=x\\ swap ~x~and~y\\ \huge\underline{y=e^x-3}} \end{matrix}\)$