Unformatted text preview: 139 or 140 Sasquatch in Portage County in 2008.
12. (a) 0.785 = 0, 117 = 117, −2.001 = −3, and π + 6 = 9 1.6 Function Arithmetic 1.6 55 Function Arithmetic In the previous section we used the newly deﬁned function notation to make sense of expressions
such as ‘f (x) + 2’ and ‘2f (x)’ for a given function f . It would seem natural, then, that functions
should have their own arithmetic which is consistent with the arithmetic of real numbers. The
following deﬁnitions allow us to add, subtract, multiply and divide functions using the arithmetic
we already know for real numbers.
Suppose f and g are functions and x is an element common to the domains of f and g .
• The sum of f and g , denoted f + g , is the function deﬁned by the formula:
(f + g )(x) = f (x) + g (x)
• The diﬀerence of f and g , denoted f − g , is the function deﬁned by the formula:
(f − g )(x) = f (x) − g (x)
• The product of f and g , denoted f g , is the function deﬁned by the formula:
(f g )(x) = f (x)g (x)
• The quotient of f and g , denoted f
, is the function deﬁned by the formula:
g (x) = f (x)
g (x) provided g (x) = 0.
In other words, to add two functions, we add their outputs; to subtract two functions, we subtract
their outputs, and so on. Note that while the formula (f + g )(x) = f (x) + g (x) looks sus...
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