Solve the problem.
-To what new value should $\mathrm { f } ( 1 )$ be changed to remove the discontinuity?
$f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } + 5 , & x < 1 \\4 , & x = 1 \\x + 5 , & x > 1\end{array} \right.$

Question

Solve the problem.
-To what new value should $\mathrm { f } ( 1 )$ be changed to remove the discontinuity?
$f ( x ) = \left\{ \begin{array} { l l } 
x ^ { 2 } + 5 , & x < 1 \
4 , & x = 1 \
x + 5 , & x > 1
\end{array} \right.$
A) 6
B) 5
C) 7
D) 4

Quizplus · Accepted Answer

To remove the discontinuity at $x=1$, we need to make sure the function is continuous at $x=1$. Therefore, we need to find out what value $f(1)$ approaches as $x$ approaches 1 from both sides. From the left side, $f(1)$ should approach $(1)^2+5=6$, and from the right side, $f(1)$ should approach $(1)+5=6$. Therefore, to remove the discontinuity, $f(1)$ should be changed to 6.

Solve the Problem f(1)\mathrm { f } ( 1 )f(1) Be Changed to Remove the Discontinuity

Solve the Problem $\mathrm { f } ( 1 )$ Be Changed to Remove the Discontinuity