Q. 13

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)


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


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