function

[red and white kop!]

functions f and g are defined as follows:
f(x) = x^2 (3-x), 0<=x<=2
g(x) = x^2 (3-x), 0<=x<=3
explain why f has an inverse and g does not.

i had a hard time finding the inverse of f and even then it was not a function. i am lost

 

[BigGlenntheHeavy]

f(x) has an inverse because it is one-to-one, while g(x) is not one-to-one.

 

[red and white kop!]

how did you find f^-1? i found it a square root, i.e. has a +- value! dont see how that is one-on-one

 

[BigGlenntheHeavy]

If a function is one-to-one, then it has an inverse. However this is consider an existence theorem (in some cases) as it tells you the function has an inverse, but doesn't necessarily tell you how to find it, in some cases it is virtually impossible to find.

f(x) is one-to-one, therefore it has an inverse, while g(x) is not one-to-one, so hasn't an inverse.

Hint: Graph them on their respective domains.