Q. 13

# Let f : R → R and g : R → R defined by f(x) = x^{2} 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) = x^{2}

(ii)

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(x^{2})

g o f = (x^{2} + 1) = x^{2} + 1

Clearly g o f ≠ f o g

Hence Proved

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