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Functions, 2ADV F1 EQ-Bank 24 MC

Given that  \(f(x)=\left\{\begin{array}{ll}3-(x-2)^2, & \text { for } x \leqslant 2 \\ m x+5, & \text { for } x>2\end{array}\right.\)

What is the value of \(m\) for which \(f(x)\) is continuous at  \(x=2\) ?

  1. \(1\)
  2. \(2\)
  3. \(-1\)
  4. \(-2\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text {If continuous at}\ x=2:\)

  \(3-(x-2)^2\) \(=mx+5\)
  \(3-(2-2)^2\) \(=2m+5\)
   \(2m\) \(=-2\)
  \(m\) \(=-1\)

 
\(\Rightarrow C\)

Filed Under: Further Functions and Relations (Y11), Piecewise Functions (Adv-2027) Tagged With: Band 4, smc-987-80-Continuous, syllabus-2027

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