Question

FITNESS Alejandro is a personal trainer. For his clients to gain the maximum benefit from their exercise, Alejandro calculates their maximum target heart rate using the function f(x) = 0.85(220 – x), where x represents the age of the client. Find the inverse of this function and interpret its meaning in the context of the situation.

Answer 1

1).
`f^(-1)(x)` = (200 -
`(x)/(0.85)`)

2). Inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.

Explanation:

Function representing the maximum heart rate is,

f(x) = 0.85(220 - x)

Here x = age of the client

Equation form of the function will be,

y = 0.85(220 - x)

To get the inverse of the given function, replace 'x' by 'y' and 'y' by 'x' and solve for y.

x = 0.85(220 - y)

220 - y =
`(x)/(0.85)`

y = 220 -
`(x)/(0.85)`

Now convert this equation into a function.

`f^(-1)(x)` = (200 -
`(x)/(0.85)`)

Here inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.