Mina O.

asked • 01/05/18

A cubic polynomial function F has zeros

A cubic polynomial function F has zeros of {-3, 0, 2}. Which restriction of the domain of f will allow its inverse to be a function?

A- x > -3

B- X > 0

C- x< 0

D- x> 2

1 Expert Answer


Frank C. answered • 01/05/18

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Mark M.

Frank, as you say
x = y3 + y2 - 6y
x = y(y2 + y - 6)
x = y(y + 3)(y - 2)
Why would there be any restrictions on this to be a function?


Mina O.

As far as i know, that's because the one-to-one restriction, which is only applied beyond the +2. 


Frank C.

Precisely, Mina. For the equation x = y(y + 3)(y - 2), note that x is still the input. You can input x = 0, and get three possible y-values as outputs! So it does not have that one-to-one qualification.
The reason I stopped at that equation was because I wasn't sure how to clearly and easily single it down to one answer choice taking that route.


Mark M.

The original function has zeros at -3, 0, and 2.
Relative minimums and maximums exist between -3 and 2
Choices A, B, and C describe the graph within the relative max and min.
Only D has a one-to-one correspondence.


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