Lesson Finding Inverse

Inverses of graphs are about finding symmetrical graphed lines along the identity function.
To find these inverse graphed lines, you need to switch the variables.
Example:
f(x) = 2x + 1
y = 2x + 1
x = 2y + 1
x - 1 = 2y
0.5x - 0.5 = y
0.5x - 0.5 = f^-1(x)

If you see a patter for the points of the lines, you can see that the values are switched as well.
Points for f(x): (0,1), (1,3), and (2,5)
Points for f^-1(x): (1,0), (3,1), and (5,2)
Example:
f(x) = 1/x - 1
y = 1/x - 1
x = 1/y - 1
x + 1 = 1/y
y(x + 1) = 1
y = 1/(x + 1)
f^-1(x) = 1/(x + 1)

Example:
f(x) = x^2 - 1
y = x^2 - 1
x = y^2 - 1
x + 1 = y^2
+-sqrt(x + 1) = y
+-sqrt(x + 1) = f^-1(x)

Example:
f(x) = 1/(x^2 + 2)
y = 1/(x^2 + 2)
x = 1/(y^2 + 2)
(y^2 + 2)x = 1
y^2 + 2 = 1/x
y^2 = 1/x - 2
y = +-sqrt(1/x - 2)
f^-1(x) = +-sqrt(1/x - 2)

Example:
f(x) = sqrt(x^2) - 2
y = sqrt(x^2) - 2
x = sqrt(y^2) - 2
x + 2 = sqrt(y^2)
(x + 2)^2 = y^2
+-sqrt((x + 2)^2) = f^-1(x)