What is the inverse of the function a(x) = (1)/(x) - 2

Question

What is the inverse of the function

`a(x) = (1)/(x) - 2`

Answer 1

a(x) = 1/x - 2

or

y = 1/x - 2

Switch x and y to find the inverse function

x = 1/y - 2

1/y = x + 2

y = 1 / (x + 2)

Answer

a^-1(x) = 1 / (x + 2)

Answer 2

To find the inverse, swap the x's and y's and solve for y. Remember that a(x) represents y

y =
`(1)/(x)` - 2 given

x =
`(1)/(y)` - 2 x's and y's swapped

x + 2 =
`(1)/(y)` added 2 to both sides

y(x + 2) = 1 multiplied y on both sides

y =
`(1)/(x + 2)` divided (x + 2) on both sides

Answer:
`a^(-1) (x)` =
`(1)/(x + 2)`