Let f : R → R and g : R → R defined by f(x) = x2 and g(x) = (x + 1). Show that g o f ≠ f o g.
To prove: g o f ≠ f o g
Formula used: (i) f o g = f(g(x))
(ii) g o f = g(f(x))
Given: (i) f : R → R : f(x) = x2
(ii)
We have,
f o g = f(g(x)) = f(x + 7)
f o g = (x + 7)2 = x2 + 14x + 49
g o f = g(f(x)) = g(x2)
g o f = (x2 + 1) = x2 + 1
Clearly g o f ≠ f o g
Hence Proved