f(x)={[-(x+6)^(2)-2," for ",x -2]:} Find f(-5) Answer:

Identify Boundary Condition: Identify which piece of the piecewise function to use for x = -5. Since x = -5 is equal to the boundary condition for the first piece of the function, we use the first piece of the function to evaluate f(-5).Substitute x = -5: Substitute x = -5 into the first piece of the function. The first piece is given by f(x) = -(x+6)^2 - 2. So, f(-5) = -(-5+6)^2 - 2.Simplify Expression: Simplify the expression inside the parentheses. -5 + 6 = 1, so we have f(-5) = -(1)^2 - 2.Square Value: Square the value inside the parentheses. (1)^2 = 1, so we have f(-5) = -1 - 2.Combine Terms: Combine the terms to find the value of f(-5). f(-5) = -1 - 2 = -3.

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Math Problems

Algebra 1

Negative exponents

Full solution

f(x)=\left\{\begin{array}{lll} -(x+6)^{2}-2 & \text { for } & x \leq-5 \\ -6 x-14 & \text { for } & x>-2 \end{array}\right.

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Find

f(-5)

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Answer:

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Identify Boundary Condition: Identify which piece of the piecewise function to use for $x = -5$ . $\newline$ Since $x = -5$ is equal to the boundary condition for the first piece of the function, we use the first piece of the function to evaluate $f(-5)$ .
Substitute $x = -5$ : Substitute $x = -5$ into the first piece of the function. $\newline$ The first piece is given by $f(x) = -(x+6)^2 - 2$ . So, $f(-5) = -(-5+6)^2 - 2$ .
Simplify Expression: Simplify the expression inside the parentheses. $\newline$ $-5 + 6 = 1$ , so we have $f(-5) = -(1)^2 - 2$ .
Square Value: Square the value inside the parentheses. $\newline$ $(1)^2 = 1$ , so we have $f(-5) = -1 - 2$ .
Combine Terms: Combine the terms to find the value of $f(-5)$ . $f(-5) = -1 - 2 = -3$ .