Q8 of 99 Page 42

Let f : R → R : f(x) (2x - 3) and

Show that (f o g) = IR = (g o f).


To prove: (f o g) = IR = (g o f).


Formula used: (i) f o g = f(g(x))


(ii) g o f = g(f(x))


Given: (i) f : R → R : f(x) = (2x - 3)


(ii)


Solution: We have,


f o g = f(g(x))




= x + 3 – 3


= x


= IR


g o f = g(f(x))




=


= x


= IR


Clearly we can see that (f o g) = IR = (g o f) = x


Hence Proved.


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