if F(x)=(Sqrt(2x+1)-2) find the inverse function F(^-1)(X)
I remeber that when I am looking for an inverse I am looking for a function that does the opposite of this function. So first I switch the x and y.
Then I solve for y by undoing operations to get the y by itself.
`+2 +2 `
`-1 = -1`
We have to solve an equation y=sqrt(2x+1)-2 for x. It is easy:
y+2 = sqrt(2x+1),
(y+2)^2 = (2x+1),
x = (1/2)*[(y+2)^2 - 1].
We must also note that the original y(x) has values from -2 to +infinity, therefore x(y) is defined for y>=-2 only.