Let $a, b, c, d$ be non-zero real numbers such that the function $f(x) = \frac{ ax+b} { cx+d}$ defined on $\mathbb{R} \backslash \{ - \frac{d}{c} \}$ has the following properties:

1) $f(19) = 19$

2) $f(97) = 97$

3) $f(f(x) ) = x$

Suppose that there is a unique number $\alpha$ such that $\alpha \neq f(x)$ for any real number $x$. What is the value of $\alpha$?

×

Problem Loading...

Note Loading...

Set Loading...