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Numerade Educator

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Problem 25 Easy Difficulty

Find a formula for the inverse of the function.

$ y = \ln (x + 3) $

Answer

$y=e^{x}-3 .$ So $f^{-1}(x)=e^{x}-3$

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Video Transcript

Let's find the inverse of the function. So we start by switching X and Y, and that gives us X equals the natural log of Y plus three. Now we went to isolate. Why Remember that natural log is law based E. You could even write it that way if it helps you. And now let's change this to its exponential form. This is equivalent to e to the X equals Y plus three. And now to isolate why we're going to subtract three from both sides So we hav e to the X minus three equals. Why now? We could rename this as f inverse of X so f inverse of X equals e to the X minus three.