f(x)={[-(x-2)^(2)+3," for ",x < 2],[-3," for ",x=2],[-2x+7," for ",2 < x <= 6]:} Find f(4) Answer:

Determine x = 4: Determine which piece of the piecewise function applies to x = 4. The function f(x) is defined by three pieces: - -(x-2)^2 + 3 for x < 2 - -3 for x = 2 - -2x + 7 for 2 < x <= 6 Since 4 is greater than 2 and less than or equal to 6, the third piece of the function applies.Substitute x = 4: Substitute x = 4 into the third piece of the function. The third piece of the function is -2x + 7. We substitute x = 4 into this expression to find f(4). f(4) = -2(4) + 7Calculate f(4): Calculate the value of f(4). f(4) = -2(4) + 7 f(4) = -8 + 7 f(4) = -1

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Math Problems

Algebra 1

Negative exponents

Full solution

f(x)=\left\{\begin{array}{lll} -(x-2)^{2}+3 & \text { for } & x<2 \\ -3 & \text { for } & x=2 \\ -2 x+7 & \text { for } & 2<x \leq 6 \end{array}\right.

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Find

f(4)

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Answer:

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Determine $x = 4$ : Determine which piece of the piecewise function applies to $x = 4$ . $\newline$ The function $f(x)$ is defined by three pieces: $\newline$ - $- (x - 2)^2 + 3$ for x < 2 $\newline$ - $-3$ for $x = 2$ $\newline$ - $-2x + 7$ for 2 < x \leq 6 $\newline$ Since $4$ is greater than $x = 4$ $0$ and less than or equal to $x = 4$ $1$ , the third piece of the function applies.
Substitute $x = 4$ : Substitute $x = 4$ into the third piece of the function. $\newline$ The third piece of the function is $-2x + 7$ . We substitute $x = 4$ into this expression to find $f(4)$ . $\newline$ $f(4) = -2(4) + 7$
Calculate $f(4)$ : Calculate the value of $f(4)$ .
$f(4) = -2(4) + 7$
$f(4) = -8 + 7$
$f(4) = -1$