Unformatted text preview: sed to transform f (x) = x3 into F (x) = − 1 (2x − 7)3 + 1?
What is the proper order of composition?
8. Write the following as a composition of two or more non-identity functions.
(a) h(x) =
(b) r(x) = √ (c) F (x) = x2 − 1 2x − 1 2
5x + 1 9. Write the function F (x) = (d) R(x) = 3 2x3 + 1
x3 − 1 x3 + 6
as a composition of three or more non-identity functions.
x3 − 9 10. The volume V of a cube is a function of its side length x. Let’s assume that x = t + 1 is
also a function of time t, where x is measured in inches and t is measured in minutes. Find
a formula for V as a function of t.
11. Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour
x is given by x(t) = −4t2 + 20t + 92, where t is the number of hours since 10 AM, 0 ≤ t ≤ 4.
(a) Find an expression for the revenue per hour R as a function of x.
(b) Find and simplify (R ◦ x) (t). What does this represent?
(c) What is the revenue per hour at noon?
12. Discuss with your classma...
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