Question

Please answer those questions​

Answer 1

Real linear function

So let f(x) = ax + b

f( f(x)) = a( ax+ b) + b

= a^2 x + ab + b

f( f( x)) = x + f( x)

a^2 x + ab + b = x + ax + b

a^2 x + ab = x + ax

a^2 x + ab = x( 1 + a)

As x can take any value

So a^2 = 1 + a, ab = 0

a^2 - a -1 = 0

As here a not equal to 0 So b= 0

and a has 2 values

So 2 functions possible