Problem
QUESTION 13 - 1 POINT Evaluate $f(x)=-3 e^{-x+1}-1$ for $x=-2$. (Round your answer to four decimal places, if necessary.) Provide your answer below:
Solution
Step 1 ：Given the function \(f(x)=-3 e^{-x+1}-1\), we are asked to evaluate it for \(x=-2\).
Step 2 ：Substitute \(x=-2\) into the function to get \(f(-2)=-3 e^{-(-2)+1}-1\).
Step 3 ：Calculate the exponential part \(e^{-(-2)+1}=e^{3}\).
Step 4 ：Substitute \(e^{3}\) back into the function to get \(f(-2)=-3 e^{3}-1\).
Step 5 ：Calculate the result to get \(f(-2)=-61.256610769563004\).
Step 6 ：Round the result to four decimal places to get \(-61.2566\).
Step 7 ：Final Answer: The value of \(f(x)=-3 e^{-x+1}-1\) for \(x=-2\) is \(\boxed{-61.2566}\).
