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f(x)={[-(x+2)^(2)+5," for ",x!=-1],[3," for ",x=-1]:} Find f(-1) Answer:

f(x)={−(x+2)2+5 for x≠−13 for x=−1 f(x)=\left\{\begin{array}{lll} -(x+2)^{2}+5 & \text { for } & x \neq-1 \\ 3 & \text { for } & x=-1 \end{array}\right. \newlineFind f(−1) f(-1) \newlineAnswer:\newline

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Full solution

Q. f(x)={−(x+2)2+5 for x≠−13 for x=−1 f(x)=\left\{\begin{array}{lll} -(x+2)^{2}+5 & \text { for } & x \neq-1 \\ 3 & \text { for } & x=-1 \end{array}\right. \newlineFind f(−1) f(-1) \newlineAnswer:\newline
  1. Define Function: The function f(x)f(x) is defined piecewise, meaning it has different expressions for different values of xx. We need to determine which expression to use for x=−1x = -1.
  2. Given Value for x=−1x = -1: According to the definition of f(x)f(x), there is a specific value given for f(x)f(x) when x=−1x = -1. The function explicitly states that f(−1)=3f(-1) = 3.
  3. Conclusion: Since the function provides a direct value for f(−1)f(-1), we do not need to perform any calculations or use the other expression for f(x)f(x). We can simply state that f(−1)=3f(-1) = 3.

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