Height and Weight The formula W=(25)/(7) h-(800)/(7) approximates the recommended minimum weight

step 1 So here we're given our formula, w equals twenty -five divided by seven, h minus 800 divided by

Height and Weight The formula W=(25)/(7) h-(800)/(7)...

Height and Weight The formula $W=\frac{25}{7} h-\frac{800}{7}$ approximates the recommended minimum weight for a person $h$ inches tall, where $62 \leq h \leq 76.$ (a) What is the recommended minimum weight for someone 70 inches tall? (b) Does $W$ represent a one-to-one function? (c) Find a formula for the inverse. (d) Evaluate the inverse for 150 pounds and interpret the result. (e) What does the inverse compute?

Height and Weight The formula $W=\frac{25}{7} h-\frac{800}{7}$ approximates the recommended minimum weight for a person $h$ inches tall, where $62 \leq h \leq 76.$
(a) What is the recommended minimum weight for someone 70 inches tall?
(b) Does $W$ represent a one-to-one function?
(c) Find a formula for the inverse.
(d) Evaluate the inverse for 150 pounds and interpret the result.
(e) What does the inverse compute?

Key Concepts

Linear Functions

Linear functions are mathematical expressions that model relationships where there is a constant rate of change between two variables. These functions are typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept. In many real-world scenarios, such as approximating weight based on height, linear functions effectively capture proportional relationships.

Function Evaluation

Function evaluation involves substituting a particular value from the domain into a function to find the corresponding output. This process is central to determining specific outcomes, verifying the behavior of the function at given points, and making predictions based on the model.

One-to-One Functions

A one-to-one function, also known as an injective function, is one in which every element in the domain corresponds to a unique element in the range. This property means no two different inputs produce the same output, which is a crucial prerequisite for the existence of an inverse function.

Inverse Functions

An inverse function reverses the operation of the original function by swapping its input and output. It provides a method to retrieve the original input when the output is known. The inverse exists only for one-to-one functions, as these allow for unambiguous reverse mapping.

Interpreting the Inverse

Interpreting the inverse function involves understanding what the computed input value signifies in the context of the problem when a specific output is given. In practical situations, this means determining the original condition that would result in the observed outcome, such as finding a corresponding height given a weight.

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