Composition of Functions Answers

A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function m(x), where x is the length of the radius of the circle in feet. The homeowner estimates that he will pay $1.50 per square foot of mulch. This cost is represented by the function g(m), where m is the area requiring mulch. Which expression represents the cost of the mulch based on the radius of the circle?

If h(x) = 5 + x and , which expression is equivalent to ?

If and , what is the range of ?

If h(x) = x – 7 and g(x) = x2, which expression is equivalent to ?

If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to ?

If p(x) = 2x2 – 4x and q(x) = x – 3, what is ?

If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to ?

If h(x) = 6 – x, what is the value of ?

If and h(x) = 4 – x, what is the value of ?

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which of the following describes the domain of ?