Suppose that X is a random variable with distribution function $\displaystyle F_X(t)$ and let $\displaystyle Y=a+bX \ \ \ b<0 $. Derive the distribution function for Y.

My solution:

I know that $\displaystyle F_Y(t)=P(T \leq t)=P(a+bX \leq t)$

$\displaystyle =P(X \geq \frac {t-a} {b} ) =1 - P( X \leq \frac {t-a}{b})=1- F_X ( \frac {t-a}{b} ) $

But the answer is wrong, why?

Thanks.