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Numerade Educator

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Problem 17 Easy Difficulty

If $ g(x) = 3 + x + e^x $ , find $ g^{-1} (4) $.

Answer

$g^{-1}(4)=0$

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Video Transcript

here we have G of X, and we're looking for G Inbursa four. So let's suppose that G Anversa for was X. That means that G of X is for because the inputs and a function are the outputs of the embers and vice versa. So what we're really doing is we're wanting to find out where G of X is equal to four. So four equals three plus X plus e to the X, and we could subtract three from both sides and we get one equals X plus each of the X. Now, we know there's only one number that makes this true. Since this function has an inverse, it must be 1 to 1. And if we just stop and look at it and think about it for a minute, we can solve by inspection. So how are we going to get the number one here? Well, what if X is zero? You know what? Each of the zero is right. Each of the zero is one, and so we would have one equals zero plus one, so that would work. So if X equals zero, we have the solution