Composition of Functions and Modeling

Consider the composite function g(f(x))=x√6. If f(x) = 3x^2, what is g(x)?

A) g(x)=√2x

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

D) They are not commutative, because f(g(x)) and g(f(x) are not equal.

The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of the completely inflated balloon is 784π cm2, how long will it take for the balloon to fully inflate?Use SA=4πr2

A) 7 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?

A) E(m) = 2,000 + 0.15(m - 20,000)

The function h(x)=(4/3)x-1 represents the composite h(x) = f(g(x)). If f(x) = 2x - 1, what is g(x)?

A) g(x)=(2/3)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.

C) 20.8 centimeters

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?

C) C(t) = 8πt

Consider the graphs of f(x)=|x|+1 and g(x)=1/x^3. The composite functions f(g(x)) and g(f(x)) are not commutative, based on which observation?

C) The domains of f(x) and g(x) are different.

Consider the composite function f(g(x))=√1/x^2-3 . If g(x) = x2 - 3, what is f(x)?

C) f(x)=√1/x

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

D) f(x) = | 2x2 + x | and g(x) = (x + 1)