1. 1.3
NEW FUNCTIONS FROM OLD

3. +
Area of oil spilled from a tanker grows with time:
Radius is also a function of time:
Area given as a function of time:
After 5 hours, t=5,

4. Example 2: Express h(t) = (1 + t3)27 as a composition of two functions:Or

6. For example, f(x) = x4 + x2 is even because f(-x) = (-x)4 + (-x)2 = x4 + x2 = f(x)
and f(x) = x3 + x is old because f(-x) = (-x)3 + (-x) = -x3 + (-x) = -(x3 + x ) = -f(x)

7. Independent variable for f is the dependent variable for f-1 .
The domain for f is the range for f-1 and the range for f is the domain for f-1
Function f must be one-to-one for f-1 to exist.

9. Example: Consider the function y = x3 , find f-1 .
Solution: To find the inverse, we solve for x, giving x = y1/3 .
So the inverse function is f-1(y) = y1/3 or if we want to call the independent x,
f-1(x) = x1/3