2. If and g are functions, then the composite function , or composition , of g and is defined by The domain of is the set of all numbers x in the domain of such that ( x ) is in the domain of g . Composition of Functions and Domain
3. Real World Connection… Suppose that an oil tanker is leaking oil and we want to be able to determine the area of the circular oil patch around the ship. It is determined that the oil is leaking from the tanker in such a way that the radius of the circular oil patch around the ship is increasing at a rate of 3 feet per minute.
4. Suppose that an oil tanker is leaking oil and we want to be able to determine the area of the circular oil patch around the ship. It is determined that the oil is leaking from the tanker in such a way that the radius of the circular oil patch around the ship is increasing at a rate of 3 feet per minute. r(t) = the radius r of the oil patch at any time t A(r) = the area of a circle as a function of the radius r.
5. What if we wanted to determine the the area of the oil patch at any given time?
6. We would need to determine the composition of the function, or A(r (t)). In simple terms, you substitute the r(t) function into the A(r) function.
13. Step 3 Find the quotient by dividing by h . Substitute. Factor out h . Divide.
14. Caution Note : ( x + h ) is not the same as ( x ) + ( h ). For ( x ) = 2x 2 – 3x in the previous ex… but **These expressions differ by 4 xh .
