Let $f(x) = x - 3$ and $q(x) = bx +1$.  If $f(q(1)) = -3$, what is $b$?
To find $b$, I need to plug in $q(1)$ into $f(x)$ and set it equal to -3. First, I'll find $q(1)$ by substituting 1 for x in $q(x)$. That gives me $q(1) = b(1) + 1 = b + 1$. Next, I'll plug in $b + 1$ for x in $f(x)$. That gives me $f(b + 1) = (b + 1) - 3 = b - 2$. Now, I'll set $f(b + 1)$ equal to -3 and solve for b. I have $b - 2 = -3$. Adding 2 to both sides, I get $b = -3 + 2 = -1$. Therefore, $b = -1$. 