Composition of Functions and Modeling Answers

Which pair of functions represents a decomposition of f(g(x)) = | 2(x + 1)2 + (x + 1) | ?

Consider the composite function .If f(x) = 3x2, what is g(x)?

When Jose installs a new app on his phone, it creates a square icon on his home screen. The square starts with side lengths of 1 cm. The side lengths grow by 2.8 cm each second until the square reaches its maximum size. What is the perimeter of the square after 1.5 seconds? Recall that the perimeter of a shape is the sum of its side lengths.

Suppose f(x) = (5 – x)3 and, g(x) = a + x2, and f(g(x)) = (1 – x2)3. What is the value of a?

Are the compositions of f(x) = 1 and g(x) = 2 commutative? Why or why not?

A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to of its maximum volume? Use π = 3.14 and .

The function represents the composite h(x) = f(g(x)). If f(x) = 2x – 1, what is g(x)?

On a coordinate plane, f (x) curves up through (negative 2, negative 3), has an inflection point at (0, 0), and curves up through (2, 3). G (x) has 2 curves. A curve opens up and to the right in quadrant 1 and approaches the y-axis and x-axis. A curves opens down and to the left in quadrant 3 and approaches the y-axis and x-axis.

A marble dropped in still water will create circular ripples or waves. The radius of each circular wave will increase 4 centimeters per second. What is the circumference of the circle after t seconds?

Anthony sells cars. Each month, he is paid $2,000, plus a 15% commission on monthly sales above $20,000. Which function calculates his monthly earnings (E) as a function of m, his monthly sales?