One model for the ideal body weight W for men (in kilograms)...

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?

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?

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Key Concepts

Function Composition

Function composition is the process of applying one function to the results of another function, denoted as (f ? g)(x) = f(g(x)). It is used to verify the relationships between functions and their inverses as composing a function with its inverse returns the original input value.

Linear Functions

Linear functions are mathematical models that express a relationship with a constant rate of change between two variables, typically in the form f(x) = mx + b. They are essential for understanding direct proportional relationships and are used in various contexts to predict one variable based on another.

Inverse Functions

Inverse functions reverse the mapping of the original function, allowing one to retrieve the original input from the output. If a function f maps an input x to an output y, then its inverse f?¹ maps y back to x, ensuring that f(f?¹(y)) = y and f?¹(f(x)) = x. This concept is crucial for solving equations where the roles of dependent and independent variables are switched.

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