Question

If f (x) is continuous on `0-4, 2],` defined as
`f(x)=6b-3ax, "for" -4 le x lt -2`
`=4x+1," for" -2le x le2,`
find the value of `a+b.`

Answer 1

Since, the function f(x) is continuous on domain [-4,2], it is continus at x = - 2
As f(x) is continuous at x = - 2
`underset(x to -2^(-))(lim)f(x) = underset(x to 2^(+))(lim) f(x) = f(-2)" ".....(1)`
`underset(x to 2^(-))(lim)f(x) = underset(x to 2)(lim)(6b - 3ax)`
` = 6b - 3a(-2)`
`= 6b + 6a`
`underset(x to 2^(+))(lim) f(x) = underset(x to -2)(lim) (4x +1)`
` = 4(-2) +1`
` = - 8 + 1 = - 7`
From equation (1),6b + 6a = - 7
`a + b = (-7)/(b)`