Ideal Body Weight One model for the ideal body weight W for...

Ideal Body Weight One model for the ideal body weight $W$ for men (in kilograms) as a function of height $h$ (in inches) is given by the function $$ W(h)=50+2.3(h-60) $$ (a) What is the ideal weight of a 6 -foot male? (b) Express the height $h$ as a function of weight $W$. (c) Verify that $h=h(W)$ is the inverse of $W=W(h)$ by showing that $h(W(h))=h$ and $W(h(W))=W$. (d) What is the height of a male who is at his ideal weight of 80 kilograms? [Note: The ideal body weight $W$ for women (in kilograms) as a function of height $h$ (in inches) is given by $W(h)=45.5+2.3(h-60) .]$

Ideal Body Weight One model for the ideal body weight $W$ for men (in kilograms) as a function of height $h$ (in inches) is given by the function
$$
W(h)=50+2.3(h-60)
$$
(a) What is the ideal weight of a 6 -foot male?
(b) Express the height $h$ as a function of weight $W$.
(c) Verify that $h=h(W)$ is the inverse of $W=W(h)$ by showing that $h(W(h))=h$ and $W(h(W))=W$.
(d) What is the height of a male who is at his ideal weight of 80 kilograms? [Note: The ideal body weight $W$ for women (in kilograms) as a function of height $h$ (in inches) is given by $W(h)=45.5+2.3(h-60) .]$

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Key Concepts

Linear Functions

A linear function is an expression that establishes a straight-line relationship between two variables, typically represented in the form y = mx + b, where m is the constant rate of change (slope) and b is the initial value (y-intercept). This concept is fundamental in many applications where a consistent increase or decrease between related quantities is observed.

Inverse Functions

An inverse function reverses the process of the original function, essentially undoing its effect. When you apply an inverse function to the output of the original function, you recover the initial input. Understanding how to derive and use inverse functions is crucial in solving equations and in many areas of mathematical modelling.

Function Composition and Verification

Function composition involves applying one function to the results of another and is a key method for verifying that two functions are inverse to each other. By confirming that composing the original function with its candidate inverse (in either order) returns the original value, one validates that the functions correctly reverse each other’s operations.