If f(x)= cc x-4 |x-4| +a, & for x<4 a+b, & for x=4 x-4 |x-4| +b, … - Vidyadip

MCQ

If $f(x)=\left\{\begin{array}{cc}\frac{x-4}{|x-4|}+a, & \text { for } x<4 \\ a+b, & \text { for } x=4 \\ \frac{x-4}{|x-4|}+b, & \text { for } x>4\end{array}\right.$
is continuous at $x=4$, then

A
$a=1, b=1$
✓
$a=1, b=-1$
C
$a=0, b=0$
D
$a=-1, b=1$

✓

Answer

Correct option: B.

$a=1, b=-1$

(b) : Since $f(x)$ is continuous at $x=4$ So, $\lim _{x \rightarrow 4^{-}} f(x)=\lim _{x \rightarrow 4^{+}} f(x)=f(x)$ at $x=4-1+a=a+b=1+b$ Now, $a-1=a+b \Rightarrow b=-1$ and $a+b=1+b \Rightarrow a=1$ Hence, $a=1, b=-1$.

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