To find g⁻¹(x), switch the places of x and y. Rearrange the equation so that it is equal to y.
g(x) = 1/(x + 4)
x = 1/(y + 4)
x(y + 4) = (1/(y + 4))(y + 4)
x(y + 4) = 1
(x(y + 4))/x = 1/x
y + 4 = 1/x
y + 4 - 4 = 1/x - 4
y = 1/x - 4
g⁻¹(x) = 1/x - 4
For the domain, you need to look at where x is located in the equation. For this equation, x is in the denominator by itself. A fraction cannot have a denominator of 0. This means that x cannot be equal to 0. The domain is:
That is not enough information. If you look at the graphic, diagonal BD (along with point E), can be moved up and down the long diagonal and the two diagonals will still have the same length. You need to state additional information.
