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1.3. NEW FUNCTIONS FROM OLD. +. 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,. Example 2: Express h(t) = (1 + t 3 ) 27 as a composition of two functions:. Or.

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1.3

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  1. 1.3 NEW FUNCTIONS FROM OLD

  2. + 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,

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

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

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

  6. 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) = y1/3or if we want to call the independent x, f-1(x) = x1/3

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