Please help me find the inverse of the function.
The graph of the inverse of a function is the reflection
of the graph across the line whose equation is y = x which
is called the "identity line", because y and x are
identically equal on that line.
So we'll be able to check that when we finish, we first
graph the equation by getting points, plotting them and
drawing a smooth curve through them.
Now we follow the rules for finding the inverse:
1. Replace f(x) by y
2. Interchange x and y
3. Solve for y
4. Replace y by f-1(x)
1. Replace f(x) by y
2. Interchange x and y
3. Solve for y
Multiply both sides by
Get all terms in y on the right and
all others on left:
Factor out y on the right
Divide both sides by
Swap sides for convenience
4. Replace y by f-1(x)
f-1(x) =
Now let's graph this on the same set of
axes in green:
Now we'll draw in the identity line whose equation is y = x.
We'll draw it dotted just to see if the green graph is the
reflection of the dark red one in that dotted identity line:
Yes it is, so f-1(x) = must be right.
Edwin
