Review Questions Answer Key

1. $a+3b=1$.
2. $2034$.
3. $x=10^3$.
4. Domain: $x\leq 3$, Range: $y\leq 2$.
5. a. Domain of $f(x)$ is $x>1$, Domain of $g(x)$ is $x\geq 2$.
   b. $f(g(x))=\log_3(\sqrt{2x-4}-1)$. $g(f(x))=\sqrt{2\log_3(x-1)-4}$.
   c. Domain of $f(g(x))$ is $x>2.5$. Domain of $g(f(x))$ is $x\geq 10$.
6. $y=4-\sqrt{-x+1}$.
7. $g^{-1}(f(x))=\frac{1}{\sqrt{3x+4}}+4$. Domain is $x > -\frac{4}{3}$.
8. $g(x)=-f(x-2)=-(x-2)^2$.
9. $y=-\frac{6}{x-3}+2$.