Question

Let $f\left(x\right)=\{\begin{array}{c}\frac{x-4}{|x-4|}+a,x<4\\ a+b,x=4\\ \frac{x-4}{|x-4|}+b,x>4\end{array}$. Then $f\left(x\right)$ is continuous at $x=4$ when?

• A. $a=0,b=0$
• B. $a=1,b=1$
• C. $a=-1,b=1$
• D. $a=1,b=-1$

Answer 1

The correct option is D $a=1,b=-1$

$\begin{array}{ccc}f\left(x\right)=a-1& for& x<4\\ f\left(x\right)=a+b& for& x=4\\ f\left(x\right)=b+1& for& x>4\end{array}$

for continuous function all value should be equal

$a-1=a+b=b+1$

gives $a=1,b=-1$