If `f(x)={(x-4)/(|x-4|)+a ,\ \ \ if\ x<4a+b ,\ \ \ if\ x=4(x-4)/(|x-4|)+b ,\ \ \ if\ x >4` is continuous at `x=4` , find `a ,\ b` .

Explanation

To solve the problem, we need to ensure that the function \( f(x) \) is continuous at \( x = 4 \). This means that the left-hand limit as \( x \) approaches 4, the value of the function at \( x = 4 \), and the right-hand limit as \( x \) approaches 4 must all be equal.

Given the function:
\[
f(x) =
\begin{cases}
\frac{x-4}{|x-4|} + a & \text{if } x < 4 \\
a + b & \text{if } x = 4 \\
...