2. Conuider the function $$ f(x)=\left\{\begin{array}{ll}2 x^{2}+3, & ext { if } x \leq 3 \ 3 x+B, & ext { if } x3\end{array} ight. $$ Find the value $$ B $$ such that $$ f(x) $$ is conitinuinus at $$ x=3 $$. (02 Marks)

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2. Conuider the function $$ f(x)=\left\{\begin{array}{ll}2 x^{2}+3, & 	ext { if } x \leq 3 \ 3 x+B, & 	ext { if } x>3\end{array}ight. $$ Find the value $$ B $$ such that $$ f(x) $$ is conitinuinus at $$ x=3 $$. (02 Marks)

Martinez Brooks · Accepted Answer

To make the function $$ f(x) $$ continuous at $$ x = 3 $$, set the left-hand limit equal to the right-hand limit at that point. Calculating both: - Left-hand limit: $$ 2(3)^2 + 3 = 21 $$ - Right-hand limit: $$ 3(3) + B = 9 + B $$ Setting them equal: $$ 21 = 9 + B $$ leads to $$ B = 12 $$. **Answer:** $$ B = 12 $$

2. Conuider the function \( f(x)=\left\{\begin{array}{ll}2 x^{2}+3, & \text { if } x \leq 3 \\ 3 x+B, & \text { if } x>3\end{array}\right. \) Find the value \( B \) such that \( f(x) \) is conitinuinus at \( x=3 \). (02 Marks)

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2. Conuider the function \( f(x)=\left\{\begin{array}{ll}2 x^{2}+3, & \text { if } x \leq 3 \\ 3 x+B, & \text { if } x>3\end{array}\right. \) Find the value \( B \) such that \( f(x) \) is conitinuinus at \( x=3 \). (02 Marks)

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