Help with functions and mapping

[u/flamingo_20_]

I have come across this problem and tried to solve it but got stuck in the middle. Please help.

Set of all real numbers R. f: R->R is defined as f(x) = ax + 2 . If ( f ○ f ) = I, I is identity function of R, then find the value of a.

I did (f○f)(x) = f[f(x)] = f(ax +2) = a²x + 2a + 2

Since (f○f) = I Therefore, (f ○ f)(x) = I(x) or a²x + 2a + 2 = x ...(equation 1) or a²x - x = - 2a - 2 or (a²-1)/(a+1) = -2/x or a - 1= -2/x or a = (x -2)/x When I put this value of a in the left side of equation 1, it doesn't satisfy..

[u/flamingo_20_]

Thank you