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1.5--Day 4--Composition of Functions
What you should learn: To find the composition of one function
with another function and to determine the domain of the
Why you should learn it: Composition of functions can be used to
model and solve real-life problems like to determine the price of a
new hybrid car.
Another way of combining two functions is to form the
composition of one with the other.
Composition is when you substitute one function in for the
variable of another function.
EX: If f(x) = x2 and g(x) = x+1, then the composition of f with g is given by
The notation for the composition of f(g(x)) is
EX: Given find the following.
EX: Given find the following.
EX: Find two functions f and g such that EX: Determine the domain of (a) f, (b) g, and (c) 1.
EX: Bacteria Count
The number of bacteria in a refrigerated food is given by
where T is the temperature of the food. When the food is removed from refrigeration, the temperature is given by
where t is the time in hours. Find
a. the composite and interpret its meaning in context of the problem
b. The bacteria count will reach 2000 when Solve
this equation to find when the count will reach 2000.
HW p. 171 51, 53, 55, 57, 71, 75, 77­79, 81, 87 = 11 problems