MAT150 College Algebra

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• MAT150 College Algebra

Section 2.4Composite and Inverse Functions
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Composition of Functions
The output of one function is the input of
another function. Example Let f(x) 5 2x
and g(x) x2 x 1Evaluate the
following f(g(2)) g(f(3)) f(g(x))
g(f(x))
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Composition of Functions
Evaluate the following f(g(1)) h(f(3))
g(f(0)) h(h(1))
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The radius, r, in centimeters, of a melting
snowball is given by r(t) 50 2.5t, where t
is the time in hours. The snowball is spherical,
with volume Find a formula for V(t), the volume
of the snowball as a function of time.
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Inverse Functions An inverse function reverses
the process of a function.
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Facts About Inverse Functions

• The inputs and outputs switch
• Domain of f Range of f -1 andRange of f
  Domain of f -1
• If the point (a,b) lies on the graph of f then
  (b,a) is on the graph of f -1
• What happens if you compose a function with its
  inverse?
• f(f -1(x)) ? f
  -1(f(x)) ?

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Inverse Functions

• The formula Cf(r)2pr gives the circumference of
  a circle of radius r.
• Find a formula for the inverse function, f-1(C),
  giving the radius as a function of circumference.
• Find and interpret the following f(10),
  f-1(10)