We start with the function \( f(x) = \log(x + 3) \).
We express the function in terms of \( y \): \[ y = \log(x + 3) \]
Next, we interchange \( x \) and \( y \): \[ x = \log(y + 3) \]
Using the property of logarithms, we rewrite the equation in exponential form: \[ e^x = y + 3 \]
Now, we solve for \( y \): \[ y = e^x - 3 \]
The inverse function is given by: \[ \boxed{f^{-1}(x) = e^x - 3} \]
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