The function f(x) is defined as follows : `therefore f(x)={:{(4x+a ","x lt 1),(6 ", " x=1),(3x-b","x gt 1):}`
If f(x) is continuous at x=1 , find the value of a and b.

Explanation

At x=1
f(1) =6
R. H.L `=underset(xrarr1^+)lim f(x)==underset(xrarr0)limf(1+h)`
`=underset(hrarr0)lim{3(1+h)-b}=3-b`
L.H.L `=underset(xrarr1^-)lim f(x)=underset(xrarr0)limf(1-h)`
`underset(hrarr0)lim{4(1-h)+a}=4+a`
`therefore` f(x) is continuous at x=1
`therefore` R.H.L =f(1)=L.H.L
`rArr` 3-b=6=4+a
`rArr` b=-3 and a=2.