Let $f ( x ) = \left\{ \begin{array} { l l } 1 - x & x < 0 \\1 + x & x > 0\end{array} \right.$ Then ƒ is continuous at 0 if ƒ(0) is defined as

Question

Let $f ( x ) = \left\{ \begin{array} { l l } 
1 - x & x < 0 \
1 + x & x > 0
\end{array} \right.$ Then ƒ is continuous at 0 if ƒ(0) is defined as

A)-2
B)-1
C)0
D)1
E)2

Quizplus · Accepted Answer

For a function to be continuous at a point, the limit from the left must equal the limit from the right, and both must equal the function's value at that point. As $x$ approaches 0 from the left, $f(x) = 1 - x$ approaches 1. As $x$ approaches 0 from the right, $f(x) = 1 + x$ also approaches 1. Therefore, defining $f(0) = 1$ makes $f$ continuous at 0.

Let f(x)={1−xx<01+xx>0f ( x ) = \left\{ \begin{array} { l l } 1 - x & x < 0 \\1 + x & x > 0\end{array} \right.f(x)={1−x1+x​x<0x>0​

Let $f ( x ) = \left\{ \begin{array} { l l } 1 - x & x < 0 \\1 + x & x > 0\end{array} \right.$