Q8 of 82 Page 126

If then let us show that, f(a) + f(b) = f(a + b)

We have



Let us simplify it,



⇒


⇒


⇒ f(x) = x …(i)


To show, f(a) + f(b) = f(a + b)


Take LHS: f(a) + f(b)


Just replace x by a in equation (i),


f(a) = a


Now, replace x by b in equation (i),


f(b) = b


LHS: f(a) + f(b)


⇒ f(a) + f(b) = a + b …(ii)


Now, Put (a + b) in equation (i),


f(a + b) = a + b


Replace (a + b) in equation (ii) from f(a + b), we get


f(a) + f(b) = f(a + b)


Thus, shown that f(a) + f(b) = f(a + b).


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