X(3), or X to the third power.
Is it one to one function?
According to the mean value theorem, there exist derivate (f(0))= 0. For this reason, there exist value f(a)=f(b).
is it one to one function?
2007-11-29 04:49:12 · 1 answers · asked by ilsup y 1 in Science & Mathematics ➔ Mathematics
Yes, it is. For every x, there is exactly one y such that y = x^3, and for every y, there is exactly one x such that x = y^(1/3). Obviously, f(0) = 0. The first response is not correct.
2007-11-29 05:00:58 · answer #1 · answered by Anonymous · 0⤊ 0⤋
You have misinterpreted the Mean Value Theorem. The derivative is 3x^2, which is always positive except at x = 0, so the function is always increasing, hence is 1-1.
2007-11-29 05:56:34 · answer #2 · answered by Tony 7 · 0⤊ 0⤋
Only even powers are 1 to 1 functions
2007-11-29 04:53:12 · answer #3 · answered by Anonymous · 1⤊ 1⤋