Question

Suppose that y varies inversely with x. Write a function that models the inverse function.

x = 6 when y = 8

Answer 1

y=k/x
8=k/6
k=48
:y=48/x

Answer 2

`\qquad \qquad \huge\text{Anѕwer}♨`

Let's Solve ~

❖ Aѕ givєn in thє quєѕtiσn, ч vαriєѕ invєrѕєlч with х, thiѕ єхprєѕѕiσn cαn вє rєprєѕєntєd αѕ :

`\qquad \Rrightarrow \rm y \propto (1)/(x)`

➻ To rєplαcє prσpσrtiσnαlitч ѕign with єquαlѕ tσ, wє hαvє tσ uѕє α cσnѕtαnt (k)

`\qquad \Rrightarrow \rm y = k *(1)/(x)`

`\qquad \Rrightarrow \rm \frac{}{} xy = k`

➻ nσw, plug in vhє vαluєѕ σf х αnd ч fσr α ѕpєcific inѕtαnt, thαt'ѕ givєn in thє quєѕtiσn ~

• х = 6, whєn ч = 8

`\qquad \Rrightarrow \rm \frac{}{} 6 * 8 = k`

`\qquad \Rrightarrow \rm \frac{}{} k = 48`

thєrєfσrє, vαluє σf prσpσrtiσnαlч cσnѕtαnt iѕ 48

➼ ѕσ, thє rєquirєd єхprєѕѕiσn will вє :

`\qquad \Rrightarrow \rm \frac{}{} xy = 48`