If f(x)=log(x+1), what is `f^(-1)`(3) ?

Options

A. 0.6
B. 4
C. 999
D. 1001

Explanation

To find \( f^{-1}(3) \) given that \( f(x) = \log(x + 1) \), we will follow these steps:

### Step 1: Set up the equation
We know that \( f^{-1}(3) \) means we need to find \( x \) such that:
\[ f(x) = 3 \]
This translates to:
\[ \log(x + 1) = 3 \]

### Step 2: Convert the logarithmic equation to exponential form
To eliminate the logarithm, we convert the equation from logarithmic form to exponential form:
\[ x + 1 = 10^3 \]

### Step 3: Calculate \( 10^3 \)
Calculating \( 10^3 \):
\[ 10^3 = 1000 \]
So we have:
\[ x + 1 = 1000 \]

### Step 4: Solve for \( x \)
Now, we solve for \( x \) by subtracting 1 from both sides:
\[ x = 1000 - 1 \]
\[ x = 999 \]

### Step 5: Conclusion
Thus, we find that:
\[ f^{-1}(3) = 999 \]

### Final Answer
The value of \( f^{-1}(3) \) is \( 999 \).

---