Stitz-Zeager_College_Algebra_e-book

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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. Function Arithmetic 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 f 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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