Question

Find the inverse of the function

f(x) = 7x-4/ x+3

A) This function is not one to one and therefore it has no inverse

B) f^-1 (x) = -3x - 4 / x - 7

C) f^-1 (x) = x + 3 / 7x - 4

D) f^-1 (x) = 3x + 4 / x+7

Answer 1

Option B -
`f^(-1)(x)=(-4-3x)/(x-7)`

Explanation:

Given :
`f(x)=(7x-4)/(x+3)`

To find : Find the inverse of the function ?

Solution :

Let y=f(x)

`y=(7x-4)/(x+3)`

Replace y with x,

`x=(7y-4)/(y+3)`

`x(y+3)=7y-4`

`xy+3x=7y-4`

`xy-7y=-4-3x`

`y(x-7)=-4-3x`

`y=(-4-3x)/(x-7)`

i.e.
`f^(-1)(x)=(-4-3x)/(x-7)`

Therefore, Option B is correct.

Answer 2

we are given

function as

`f(x)=(7x-4)/(x+3)`

step-1: Set f(x)=y

`y=(7x-4)/(x+3)`

step-2: Switch x and y

`x=(7y-4)/(y+3)`

step-3: Solve for y

now, we can solve for y

`x(y+3)=7y-4`

`xy+3x=7y-4`

`xy=7y-4-3x`

`xy-7y=-4-3x`

`y(x-7)=-4-3x`

`y=(-4-3x)/(x-7)`

so, we get

`f^(-1)(x)=(-3x-4)/(x-7)`...............Answer