Given, $f(x) = ax+b$ -----→ 1
$f(bx + a) = x$ -----→ 2
Using (1), we get
$f(bx + a) = a(bx+a)+b$ ----→ 3
From (2) and (3),
$a(bx + a) + b = x$
=> $abx + a^{2} + b = x$ ---→ 4
Now, put x=0 in (4)
=> $a^{2} + b = 0$ ------→ 5
put x=1 in (4)
$ab + a^{2} + b = 1$
=> $ab = 1$ ---→ (Using 5)
Now, you have 2 equations and 2 variables
$a^{2} + b = 0$
$ab = 1$
Solve the above 2 equations, you will get a = -1 and b = -1
Hence, a + b = -1 + (-1) = -2