1.

Findthe values of a and bsucht that thefunction fdefined by fx = {{:((x-4)/(|x-4|)+a, if x lt 4),(a+b,if x=4),((x-4)/(|x-4|)+b, if x gt 4):} is a continousfunctionat x = 4 .

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SOLUTION :We have, We have, `fx = {{:((X-4)/(|x-4|)+a, if x lt 4),(a+B,if x=4),((x-4)/(|x-4|)+b, if x GT 4):}`
At `x = 4, LHL =underset(xrarr4^(-))(lim)(x-4)/(|x-4|)+a`
`= underset(hrarr0)(lim)(4-h-4)/(|4-h-4|)+a= underset(hrarr0)(lim)(-h)/(h) +a`
`= -1 +a`
`RHL = underset(xrarr4^(+))lim(x-4)/(|x-4|)+b`
`= underset(hrarr0)(lim)(4+h-4)/(|4+h-4|) +b = underset(hrarr0)(lim)(h)/(h)+b = 1+b`
`f(4)=a + b RARR -1+b = a+ b`
`rArr -1 +a = a+b` and `1+b= a+ b`
`:. b = - 1` and `a =1`.


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