Let *𝑓*f be the function

*𝑓*(*𝑥*)=6*𝑥*−1*𝑎𝑥*+*𝑏*8*𝑥*−1for *𝑥*<−1for −1≤*𝑥*≤12for *𝑥*>12


It seems that the function \( f(x) \) you provided is piecewise, but the formatting got mixed up. Let's clarify the function in a proper format. 

If the function \( f(x) \) is defined as:

\[
f(x) = 
\begin{cases} 
6x - 1 & \text{for } x < -1 \\
ax + b & \text{for } -1 \leq x \leq 1 \\
8x - 1 & \text{for } x > 1
\end{cases}
\]

Let me know if this is the correct function. If so, we can proceed with finding conditions on \( a \) and \( b \) to make this function continuous at \( x = -1 \) and \( x = 1 \).

Explore the concept of piecewise functions with a detailed example. This problem involves clarifying and defining a piecewise function with conditions for continuity. Suitable for advanced high school students and those preparing for calculus.

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