{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


State the restricted domain 2 find and interpret p1

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: hich our last example illustrates. Example 5.1.3. Write each of the following functions as a composition of two or more (non-identity) functions. Check your answer by performing the function composition. 1. F (x) = |3x − 1| 2. G(x) = x2 2 +1 √ x+1 3. H (x) = √ x−1 Solution. There are many approaches to this kind of problem, and we showcase a different methodology in each of the solutions below. 1. Our goal is to express the function F as F = g ◦ f for functions g and f . From Definition 5.1, we know F (x) = g (f (x)), and we can think of f (x) as being the ‘inside’ function and g as being the ‘outside’ function. Looking at F (x) = |3x − 1| from an ‘inside versus outside’ perspective, we can think of 3x − 1 being inside the absolute value symbols. Taking this cue, we define f (x) = 3x − 1. At this point, we have F (x) = |f (x)|. What is the outside function? The function which takes the absolute value of its input, g (x) = |x|. Sure enough, (g ◦ f )(x) = g (f (x)) = |f (x)| = |3x − 1| = F (x), so we are done. 288 Further Topics in Functions 2. We at...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online