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f(x)={[-4x," for ",x < -1],[-x+1," for ",-1 <= x <= 3],[-2x+8," for ",x > 3]:}
Find
f(3)
Answer:

$f(x)=\left\{\begin{array}{lll} -4 x & \text { for } & x<-1 \\ -x+1 & \text { for } & -1 \leq x \leq 3 \\ -2 x+8 & \text { for } & x>3 \end{array}\right.$ $\newline$ Find $f(3)$ $\newline$ Answer: $\newline$

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Solve absolute value inequalities

Full solution

Q.

f(x)=\left\{\begin{array}{lll} -4 x & \text { for } & x<-1 \\ -x+1 & \text { for } & -1 \leq x \leq 3 \\ -2 x+8 & \text { for } & x>3 \end{array}\right.

\newline

Find

f(3)

\newline

Answer:

\newline

Identify Function Piece: Since $3$ is within the range $-1 \leq x \leq 3$ , we use the second piece of the function, which is $f(x) = -x + 1$ .
Substitute $x = 3$ : Now we substitute $x = 3$ into the function: $f(3) = -(3) + 1$ .
Perform Calculation: Perform the calculation: $f(3) = -3 + 1 = -2$ .

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