Question

F(x)= 2x+7/x+1 . what is the inverse of this function?

Answer 1

Hey there :)

f ( x ) is also y
So
`f(x)= (2x+7)/(x+1)` is
`y = (2x+7)/(x+1)`

To find the inverse, reverse the places of x and y, let y be in the place of x and x in the place of y
↓

`x = (2y+7)/(y+1)`
x ( y + 1 ) = 2y +7
xy + x = 2y + 7
xy - 2y = 7 - x

Take y as common factor
y ( x - 2 ) = 7 - x

Divide by x - 2 on either side to isolate y and thus find the inverse

`(y(x-2))/((x-2)) = (7-x)/(x-2)`
y =
`(7-x)/(x-2)`

Therefore the inverse of the function is:
f ⁻¹ ( x ) =
`(7-x)/(x-2)`

Answer 2

`f(x) = (2x+7)/(x+1)`


`\text {Let y = }f(x),`


`y= (2x+7)/(x+1)`


`y(x + 1) = 2x + 7`


`xy + y = 2x + 7`


`xy - 2x = 7 - y`


`x(y - 2) = 7 - y`


`x = (7-y)/(y-2)`


`f^(-1)(x) = (7-x)/(x-2)`