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Given the function f, evaluate f(-1),f(0),f(2), and f(4). f(x)={[x^(2)-3," if "x < 2],[4+|x-6|," if "x >= 2]:} {:[f(-1)=" Number "],[f(0)=" Number "],[f(2)=" Number "],[f(4)=" Number "]:}

Given the function f f , evaluate f(−1),f(0),f(2) f(-1), f(0), f(2) , and f(4) f(4) .\newlinef(x)={x2−3 if x<24+∣x−6∣ if x≥2 f(x)=\left\{\begin{array}{cc} x^{2}-3 & \text { if } x<2 \\ 4+|x-6| & \text { if } x \geq 2 \end{array}\right. \newlinef(−1)= f(0)= f(2)= f(4)= \begin{aligned} f(-1) & =\ \\ f(0) & =\ \\ f(2) & =\ \\ f(4) & =\\ \end{aligned}

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Full solution

Q. Given the function f f , evaluate f(−1),f(0),f(2) f(-1), f(0), f(2) , and f(4) f(4) .\newlinef(x)={x2−3 if x<24+∣x−6∣ if x≥2 f(x)=\left\{\begin{array}{cc} x^{2}-3 & \text { if } x<2 \\ 4+|x-6| & \text { if } x \geq 2 \end{array}\right. \newlinef(−1)= f(0)= f(2)= f(4)= \begin{aligned} f(-1) & =\ \\ f(0) & =\ \\ f(2) & =\ \\ f(4) & =\\ \end{aligned}
  1. Determine f(−1)f(-1): Determine which part of the piecewise function to use for f(−1)f(-1) since −1<2-1 < 2, use f(x)=x2−3f(x) = x^2 - 3.\newlineCalculation: f(−1)=(−1)2−3=1−3=−2f(-1) = (-1)^2 - 3 = 1 - 3 = -2.
  2. Determine f(0)f(0): Determine which part of the piecewise function to use for f(0)f(0) since 0<20 < 2, use f(x)=x2−3f(x) = x^2 - 3.\newlineCalculation: f(0)=02−3=0−3=−3f(0) = 0^2 - 3 = 0 - 3 = -3.
  3. Determine f(2)f(2): Determine which part of the piecewise function to use for f(2)f(2) since 2≥22 \geq 2, use f(x)=4+∣x−6∣f(x) = 4 + |x - 6|.\newlineCalculation: f(2)=4+∣2−6∣=4+4=8f(2) = 4 + |2 - 6| = 4 + 4 = 8.
  4. Determine f(4)f(4): Determine which part of the piecewise function to use for f(4)f(4) since 4≥24 \geq 2, use f(x)=4+∣x−6∣f(x) = 4 + |x - 6|.\newlineCalculation: f(4)=4+∣4−6∣=4+2=6f(4) = 4 + |4 - 6| = 4 + 2 = 6.

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