Remember that f(x) must be one-to-one (only one y-value for each x-value) over the domain where f –1(x)is defined as a function. So, in some cases you must restrict the domain of f(x) so that it's one-to-one. There might be more than one section of domain that's one-to-one.
HINT: The function f(x) is one-to-one wherever it's monotonic ("monotonic" simply means increasing or decreasing over the entire interval, so the derivative does not change sign).
To find these intervals, start by taking the first derivative, which is AP Calculus AB Semester 2 and setting it equal to zero.
I. (–∞, –3]
II. [–3, ∞)
III. [2, ∞)
I
II
III
Either I or II
Either I or III
3 answers
I believe that it is Either I or III
Yes, it's Either 1 or 3, or answer E.
Actually, f(x) = x^3+3/2x^2-18x+4
When you differentiate to find critical points which are -3 & 2, you would see from (-infinity,-3] and [2,infinity). Those two ranges make f(x) become one-to-one function.
When you differentiate to find critical points which are -3 & 2, you would see from (-infinity,-3] and [2,infinity). Those two ranges make f(x) become one-to-one function.
2 answers