You were given:
y = 4x - x^2
We switch x and y.
x = 4y - y^2
Factor the right side of the equation.
x = y(4 - y)
Next:
xy = 4 - y
Add y on both sides of the equation.
xy + y = 4
Factor on the left side.
y(x + 1) = 4
Isolate y on the left side.
y = 4/(x + 1)
Replace y by f^-1 (x).
f^-1 (x) = 4/(x + 1)
Done!
Find the Inverse Function:
y=4x-x^2
3 answers
How did you go from here:
x = y(4 - y)
To here:
Next:
xy = 4 - y
Shouldn't you divide rather than multiply?
x = y(4 - y)
To here:
Next:
xy = 4 - y
Shouldn't you divide rather than multiply?
Mike,
After doing the question again, I realize that 4x - x^2 is not one-to-one. Hence, it has no inverse function.
Sorry....The answer is: NO INVERSE FUNCTION HERE.
After doing the question again, I realize that 4x - x^2 is not one-to-one. Hence, it has no inverse function.
Sorry....The answer is: NO INVERSE FUNCTION HERE.
2 answers