1 applies this means that if we take combinations of

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: output from f , f (x) = 3x + 4, and x substitute that into g . That is, g (f (x)) = g (3x + 4) = (3x+4)−4 = 33 = x, which is our original 3 input to f . If we carefully examine the arithmetic as we simplify g (f (x)), we actually see g first ‘undoing’ the addition of 4, and then ‘undoing’ the multiplication by 3. Not only does g undo f , but f also undoes g . That is, if we take the output from g , g (x) = x−4 , and put that into 3 f , we get f (g (x)) = f x−4 = 3 x−4 + 4 = (x − 4) + 4 = x. Using the language of function 3 3 composition developed in Section 5.1, the statements g (f (x)) = x and f (g (x)) = x can be written as (g ◦ f )(x) = x and (f ◦ g )(x) = x, respectively. Abstractly, we can visualize the relationship between f and g in the diagram below. f x = g (f (x)) y = f (x) g 294 Further Topics in Functions The main idea to get from the diagram is that g takes the outputs from f and returns them to their respective inputs, and conversely, f takes outputs...
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