We have f (x) = {

a+bx	x<1
4	x=1
b−ax	x>1

and

lim

x→1

f (x) = f (1) ... (i)
So first we have to find

lim

x→1

f (x)
Now,

lim

x→1−

f (x) =

lim

x→1−

(a + bx) = a + b
and

lim

x→1+

f (x) =

lim

x→1+

(b - ax) = b - a
Also, f (1) = 4
By (i) ,

lim

x→1−

f (x) =

lim

x→1+

f (x)
⇒ a + b = 4 ... (ii)
and b - a = 4 ... (iii)
Adding (ii) and (iii), we get 2b = 8 ⇒ b = 4
Substituting the value of b in (iii), we get 4 – a = 4 ⇒ a = 0
Thus a = 0 and b = 4.