{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

# 2x 2h 12x 1 for reasons which will become clear in

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: piciously like some kind of distributive property, it is nothing of the sort; the addition on the left hand side of the equation is function addition, and we are using this equation to deﬁne the output of the new function f + g as the sum of the real number outputs from f and g .1 Example 1.6.1. Let f (x) = 6x2 − 2x and g (x) = 3 − 1 . Find and simplify expressions for x 1. (f + g )(x) 3. (f g )(x) 2. (g − f )(x) 4. 1 g f (x) The author is well aware that this point is pedantic, and lost on most readers. 56 Relations and Functions In addition, ﬁnd the domain of each of these functions. Solution. 1. (f + g )(x) is deﬁned to be f (x) + g (x). To that end, we get (f + g )(x) = f (x) + g (x) = 6x2 − 2x + 3 − 1 x 1 x 6x3 2x2 3x 1 − + − x x x x 3 − 2x2 + 3x − 1 6x x = 6 x2 − 2x + 3 − = = get common denominators To ﬁnd the domain of (f + g ) we do so before we simplify, that is, at the step 6x2 − 2x + 3 − 1 x We see x = 0, but everything else is ﬁne. Hence, the domain is (−∞, 0) ∪ (0, ∞). 2. (g...
View Full Document

{[ snackBarMessage ]}