22. Clothing Men's shoe sizes are a linear function of foot length. a. Write an equation for a man's shoe size as a function of foot length. What men's size shoe is needed for a foot that measures 9.5 in.? Men's Shoe Sizes Foot Shoe Length (in.) Size 10 $7\frac{1}{2}$ 11 $11\frac{1}{2}$
Added by David B.
Close
Step 1
- Foot length of 10 inches corresponds to a shoe size of \(7\frac{1}{2}\). - Foot length of 11 inches corresponds to a shoe size of \(11\frac{1}{2}\). Show more…
Show all steps
Your feedback will help us improve your experience
Sanchit Jain and 98 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In the USA, the shoe sizes for men are approximated by the equation 3f - s = 24, where f (x-axis) represents the length of the foot in inches and s (y-axis) represents the shoe size. a. The average man's foot is 11.5 inches long. What is the average man's shoe size? b. Use the function to determine the x- and y-intercept. State the meaning of each in terms of this problem situation. c. Which form can most easily be used to determine the slope of this equation? Determine the slope of this equation and describe what it means in terms of the problem situation.
Lauren B.
Shoe Sizes The table shows men's shoe sizes in the United States and the corresponding European shoe sizes. Let $y=f(x)$ represent the function that gives the men's European shoe size in terms of $x,$ the men's U.S. size. $$ \begin{array}{|c|c|}\hline \text { Men's U.S. } & {\text { Men's European }} \\ \hline \text { shoe size } & {\text { shoe size }} \\ \hline 8 & {41} \\ {9} & {42} \\ {10} & {43} \\ {11} & {45} \\ {12} & {46} \\ {13} & {47} \\ \hline\end{array} $$ (a) Is $f$ one-to-one? Explain. (b) Find $f(11)$ (c) Find $f^{-1}(43),$ if possible. (d) Find $f\left(f^{-1}(41)\right)$ (e) Find $f^{-1}(f(13))$
Functions and Their Graphs
Inverse Functions
SHOE SIZES The table shows men's shoe sizes in the United States and the corresponding European shoe sizes. Let $y=f(x)$ represent the function that gives the men's European shoe size in terms of $x$, the men's U.S. size. (a) Is $f$ one-to-one? Explain. (b) Find $f(11)$. (c) Find $f^{-1}(11)$, if possible. (d) Find $f(f^{-1}(41))$. (e) Find $f^{-1}(f(13))$.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD