Let f(x)=x−3 and q(x)=bx+1. If f(q(1))=−3, what is b?
Solution — click to reveal
We have q(1)=b⋅1+1=b+1, so f(q(1))=f(b+1). Applying the definition of f, we have f(q(1))=f(b+1)=(b+1)−3=b−2. Therefore, the equation f(q(1))=−3 gives us b−2=−3, so b=−1.