Composition of Functions:
A) The function defined by f(x) = 12x computes the number of inches in 'x' feet and the function defined by g(x)= 5280x computes the number of feet in 'x' miles. What is (f of g)(x)?

B) An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the water as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the circular oil slick on the surface is r(t) = 4t feet. Let A(r) = pi(r) squared represent the area of a circle of radius r. Find and interpret (A of r)(t).

Please solve and EXPLAIN how you did it.

Question

Composition of Functions:
A) The function defined by f(x) = 12x computes the number of inches in 'x' feet and the function defined by g(x)= 5280x computes the number of feet in 'x' miles. What is (f of g)(x)?

B) An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the water as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the circular oil slick on the surface is r(t) = 4t feet. Let A(r) = pi(r) squared represent the area of a circle of radius r. Find and interpret (A of r)(t).

Please solve and EXPLAIN how you did it.

anonymous · Answer

$$ f\circ g(x)=f(g(x))=f(5280x)=12\times 5280x$$

anonymous · Answer

$$A\circ r (t)=A(4t)=\pi\times (4t)^2$$

anonymous · Answer

you can clean both up by multiplication