Composition of Functions Answers

If and , what is the range 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 ?

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

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

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 and g(x) = 5x – 4, what is the domain of ?

For which pair of functions is ?

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

If f(x) = x2 + 1 and g(x) = x – 4, which value is equivalent to ?

Fifteen percent of an employee’s taxable income is collected each paycheck. Before taxes are removed from each paycheck, $350 of tax-exempt expenses is taken out. If the variable x represents the employee’s pay before tax-exempt expenses and taxes are removed, which expression represents the employee’s take-home pay after these deductions?