Stitz-Zeager_College_Algebra_e-book

3 3 we close this section with concept of the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online