Questions: f(x) = -x^2 + 2 for x ≠ 2 -5 for x = 2 Find f(0)

Transcript text: \[ f(x)=\left\{\begin{array}{lll} -x^{2}+2 & \text { for } & x \neq 2 \\ -5 & \text { for } & x=2 \end{array}\right. \] Find $f(0)$

Solution

Step 1: Identify the value of $ x $ to evaluate

The problem asks to find $ f(0) $. Here, $ x = 0 $.

Step 2: Determine which piece of the function to use

The function $ f(x) $ is defined piecewise:

Since $ x = 0 $ and $ 0 \neq 2 $, we use the first piece of the function: $ f(x) = -x^{2} + 2 $.

Step 3: Substitute $ x = 0 $ into the function

Substitute $ x = 0 $ into $ f(x) = -x^{2} + 2 $: \[ f(0) = -(0)^{2} + 2 \]

Step 4: Simplify the expression

Calculate $ (0)^{2} $: \[ (0)^{2} = 0 \] Substitute back into the equation: \[ f(0) = -0 + 2 = 2 \]

$\boxed{2}$

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