Answer :

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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