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

f(x)={4amp; for amp;xlt;22x7amp; for amp;2xlt;72x7amp; for amp;x7 f(x)=\left\{\begin{array}{lll} -4 &amp; \text { for } &amp; x&lt;2 \\ 2 x-7 &amp; \text { for } &amp; 2 \leq x&lt;7 \\ 2 x-7 &amp; \text { for } &amp; x \geq 7 \end{array}\right. \newlineFind f(2) f(2) \newlineAnswer:\newline

Full solution

Q. f(x)={4 for x<22x7 for 2x<72x7 for x7 f(x)=\left\{\begin{array}{lll} -4 & \text { for } & x<2 \\ 2 x-7 & \text { for } & 2 \leq x<7 \\ 2 x-7 & \text { for } & x \geq 7 \end{array}\right. \newlineFind f(2) f(2) \newlineAnswer:\newline
  1. Identify Piece for x=2x=2: Identify the correct piece of the piecewise function to use for x=2x = 2. The function f(x)f(x) is defined by different expressions depending on the value of xx. We need to determine which expression applies when x=2x = 2. f(x)={4amp;for xlt;2, 2x7amp;for 2xlt;7, 2x7amp;for x7f(x) = \begin{cases} -4 &amp; \text{for } x &lt; 2,\ 2x - 7 &amp; \text{for } 2 \leq x &lt; 7,\ 2x - 7 &amp; \text{for } x \geq 7 \end{cases} Since x=2x = 2 falls into the second category (2 \leq x < 7), we will use the expression 2x72x - 7 to find f(2)f(2).
  2. Calculate f(2)f(2) Value: Calculate the value of f(2)f(2) using the correct expression.\newlineWe will substitute xx with 22 in the expression 2x72x - 7.\newlinef(2)=2(2)7f(2) = 2(2) - 7\newlinef(2)=47f(2) = 4 - 7\newlinef(2)=3f(2) = -3