Hi, how do you find the inverse of this function: ?
Hello, sakonpure6!
How do you find the inverse of this function? .
Use the prescribed procedure.
[However, the result will not be a function.]
We have: .
"Switch" variables: .
Solve for
. .
Quadratic Formula: .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
Therefore: .
Did you plot it? You'll notice that f is not bijective over it's entire domain so in order to establish an inverse you will have to restrict the domain of f to an interval, or union of intervals, where it is.
Once you've done that you can solve the quadratic equation y=f(x) for x in terms of y. This gives you x=g(y). Replace every occurrence of y in g(y) with x to obtain g(x).
for x in the restricted domain you chose.