6.6 Function Operations
Name: __________________
Objectives : Students will be able to add, subtract, multiply and
divide functions. Students will be able to find composite
functions.
Function Operations
(f + g)(x) = _________________
(f - g)(x) = _________________
(fg)(x) = __________________
(f/g)(x) = __________________
Jan 22­9:31 AM
Let f(x) = 3x2 + 4x and g(x) = 5x2 - 6x.
1.) f(x) + g(x)
2.) f(x) - g(x)=
3.) f(x)g(x)
Jan 25­12:16 PM
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Domain: What x-values can be plugged in?
The domain of any operation applied to f and are the x-values
that are in the domains of both f and g. Also, the domain of a
quotient does not include x-values for which the bottom function
equals 0.
Examples Find the domain of each function.
1.) f(x) = x3 - 4
2.) g(x) = √x + 2
3.) g(x) = x + 3
x-2
Jan 22­9:47 AM
Examples: Let f(x) = x 2 - 9 , g(x) = x + 4 , h(x) = √x
Domain of f(x):
Domain of g(x):
Domain of h(x):
Perform each operation and state the domain.
1.) f(x) + g(x)
2.) f(x) + h(x)
3.) f(x)/g(x)
4.) f(x)/h(x)
Jan 22­9:56 AM
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Examples Let f(x), g(x) and h(x) be as in the previous example.
Find the following.
1.) f(3)
2.) h(16)
3.) g(-10)
4.) f(√π)
Jan 25­12:25 PM
Composition of Functions (f o g)(x) = f(g(x))
Let f(x) = 4x + 3 and g(x) = -x 2 + 1.
Find the indicated value.
1.) f(g(1)) =
2.) g(f(-3)) =
3.) f(f(0)) =
Jan 22­10:03 AM
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Examples: Let f(x) = x2 - 9 , g(x) = x + 4 , h(x) = √x
Perform the indicated operation.
1.) g(f(x))
2.) f(g(x))
3.) h(f(x))
4.) f(h(x))
Jan 22­10:05 AM
6.6 ICE
Let f(x) = 6x + 4 and g(x) = 4x + 3.
Name: _______________
Find the following:
1.) f(x) - g(x)
1.) ____________
2.) f(x)g(x)
2.) ____________
3.) f(g(-1))
3.) ____________
4.) f(g(x))
4.) _____________
Jan 22­10:09 AM
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