Let f : R → R and g : R → R defined by f(x) = x2 and g(x) = (x + 1

1.	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.
Answer» 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)g : R → R g(x) = (x + 1) We have, f o g = f(g(x)) = f(x + 7) f o g = (x + 7)² = x ² + 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

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.

Answer»

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)g : R → R g(x) = (x + 1)

We have,

f o g = f(g(x)) = f(x + 7)

f o g = (x + 7)² = x ² + 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