Questions: Find the inverse of f(x) = log (x+3).

Find the inverse of f(x) = log (x+3).
Transcript text: 19. Find the inverse of $f(x)=\log (x+3)$.
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Solution

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Solution Steps

Step 1: Define the Function

We start with the function \( f(x) = \log(x + 3) \).

Step 2: Express in Terms of \( y \)

We express the function in terms of \( y \): \[ y = \log(x + 3) \]

Step 3: Interchange \( x \) and \( y \)

Next, we interchange \( x \) and \( y \): \[ x = \log(y + 3) \]

Step 4: Rewrite in Exponential Form

Using the property of logarithms, we rewrite the equation in exponential form: \[ e^x = y + 3 \]

Step 5: Solve for \( y \)

Now, we solve for \( y \): \[ y = e^x - 3 \]

Final Answer

The inverse function is given by: \[ \boxed{f^{-1}(x) = e^x - 3} \]

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