Question

Suppose that y varies inversely with x. Write a function that models the inverse function. x = 5 when y = 7

Answer 1

varying inversely means y=a number divided by x
find the number: 7=k/5 =>k=35
so the equation is y=35/x

Answer 2

`y=35*(1)/(x)`

Explanation:

Given : y varies inversely with x

To Find: Write a function that models the inverse function. x = 5 when y = 7

Solution:

We are given that y varies inversely with x

So,
`y \propto (1)/(x)`

`\Rightarrow y=k*(1)/(x)` ---A

where k is the constant of proportionality

Now we are given that x = 5 when y = 7

So,
`\Rightarrow 7=k*(1)/(5)`

`\Rightarrow 35=k`

Substitute the value of k in A

`\Rightarrow y=35*(1)/(x)`

Hence a function that models the inverse function is
`y=35*(1)/(x)` .