Complete each problem below by hand. Show your work and provide a reason for each step. Calculators are not allowed on this assignment.
- Let $f(x)=\sqrt{x^2+5x+6}$ and $g(x)=3x^2$. and use this to answer the following. Remember to show all steps and provide justifications.
a. Find the domain and range of $f(x)$ and $g(x)$.
b. What is the domain and range of $(f \circ g)(x)? (g \circ f)(x)$?
c. Determine the function $(g \circ f)(x)$.
d. Find the maximum or minimum of $(g \circ f)(x)$.
e. Describe the relationship between $f(x)$, $g(x)$, and $(g \circ f)(x)$.
