This shows that 
(
3)
4
y
x
−
= Define g : Y → N by
Rationalised 2023-24
RELATIONS AND FUNCTIONS
13
(
3)
( )
4
y
g y
−
= Now, gof(x) = g (f(x)) = g(4x + 3) = (4
3
3)
4
x
x
+
−
=
 and
fog(y) = f (g (y)) = f
(
3)
4 (
3)
3
4
4
y
y
−
−

 =
+




 = y – 3 + 3 = y This shows that gof = IN
and fog = IY, which implies that f is invertible and g is the inverse of f