Answer
(a) $y = f(x) = 1609.344x$
(b) $x = f^{-1}(y) = \frac{y}{1609.344}$
(c) In practical terms, $x = f^{-1}(y) = \frac{y}{1609.344}$ tells us how to convert a length in meters (y) to miles (x).
Work Step by Step
(a)
To express a length in meters (y) as a function of the same length in miles (x), we can use the formula:
$y = f(x) = 1609.344x$
This formula converts a length in miles (x) to meters (y) by multiplying it by the conversion factor $1609.344$
(b)
To find the formula for the inverse of f, we can solve for x in terms of y:
$x =f^{-1}(y) = \frac{y}{1609.344}$
So, the inverse function is $x =f^{-1}(y) = \frac{y}{1609.344}$
which converts a length in meters (y) to miles (x).
(c)
In practical terms, $x = f^{-1}(y) = \frac{y}{1609.344}$
tells us how to convert a length in meters (y) to miles (x).
If given a length in meters, we can use this formula to find the equivalent length in miles.
For example, if we have a length of $1609.344$ meters, it is equivalent to 1 mile.
