# Function problem.

• October 18th 2010, 07:47 AM
Sambit
Function problem.
Let, f:Z-->Z be a function defined by:- f(s)= as + b , for certain integers a and b. Then, for what values of a and b, f○f will be an identity map?
• October 18th 2010, 08:07 AM
NOX Andrew
I read the Wikipedia article on identity functions (assuming identity map and identity function are synonymous) and believe I can help.

$f(x)$ is an identity function if $f(x) = x$. Therefore, $f(f(s))$ is an identity function if $f(f(s)) = f(s)$.

$f(f(s)) = af(s) + b = a(as + b) + b = a^2s + ab + b
$

Solve the equation $a^2s + ab + b = as + b$ for $a$ and $b$.