The graphs of a function f(x)=3x+b and its inverse function f^-1(x) intersect at the point (-3,a). Given that b and a are both integers, what is the value of a?

Answer 1

f(x) = 3x + b
f^-1 (x) = (x - b)/3

(-3, a) lies on both
so
f(-3) = -9 + b = a
f^-1(-3) = (-3-b)/3 = a

(-3-b)/3 = -9+b
-3-b = -27 + 3b
24 = 4b
b = 6
then a = -9+6 = -3

a = -3, b = 6

check my arithmetic