Functions, 2ADV EQ-Bank 1 MC

Which of the following piecewise functions is not continuous at \(x =1\) ?

\(f(x)= \begin{cases}x^2+1, & \text{for } \ x \leq 1 \\ 3 x-1, & \text{for } x>1\end{cases}\)
\(f(x)= \begin{cases}2 x, & \text{for } \ x<1 \\ x+1, & \text{for } x \geq 1\end{cases}\)
\(f(x)= \begin{cases}-x^2, & \text{for }\ x \leq 1 \\ 2 x-1, & \text{for } x>1\end{cases}\)
\(f(x)= \begin{cases}3-x, & \text{for } \ x<1 \\ x^2+1, & \text{for } x \geq 1\end{cases}\)

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\(C\)

Show Worked Solution

\(\text {Consider option }C:\)

\(\text{As} \ \ x \rightarrow 1^{-},-x^2 \rightarrow-1\)

\(\text{As} \ \ x \rightarrow 1^{+}, 2 x-1 \rightarrow 1\)

\(\therefore \ \text {Not continuous at} \ \ x=1\)

\(\Rightarrow C\)