This lesson will teach you how to perform operations on functions. Basically, you can add, subtract, multiply, and divide functions. Let f and g be functions. Take a look at the following figure to see how we can perform these operations on a function.
How to do addition of functions
( f + g )(x) = f(x) + g(x)
Example #1
Find f + g if f(x) = 2x - 7 and g(x) = 5x + 8
(f + g)(x) = f(x) + g(x)
= 2x - 7 + 5x + 8
= 2x + 5x + - 7 + 8
= 7x + 1
How to do subtraction of functions
( f - g )(x) = f(x) - g(x)
Example #2
Find f - g if f(x) = 3x + 9 and g(x) = 6x - 3
(f - g)(x) = f(x) - g(x)
= 3x + 9 - (6x - 3)
= 3x + 9 - 6x - - 3
= 3x + 9 - 6x + 3
= 3x - 6x + 9 + 3
= -3x + 12
Notice that we were able to cancel x + 1 since x + 1 is on top and at the bottom in the rational expression.
Sep 17, 20 03:57 PM
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