Question

If $f\left(x\right)=x$, then which of the following must be true?
(a) $f(a+b)=f\left(a\right)+f\left(b\right)$
(b) $f\left(2a\right)=2f\left(a\right)$
(c) $f(-a)=-f\left(a\right)$

Answer 1

$\left(i\right)$ $f(a+b)=f\left(a\right)+f\left(b\right)$ acn be possible because.

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

$f\left(a\right)+f\left(b\right)$

$\left(ii\right)$ $f\left(2a\right)=2a[\because f(x)=x]$

$f\left(2a\right)=2f\left(a\right)$

$\left(iii\right)$$f(-a)=-a$

$f\left(a\right)=-f\left(a\right)$

Three conditions are true.