Determine the cubic function with zeros -2, 3 and 4 and f(5) = 28

f(x) = 2(x + 2)(x - 3)(x - 4) or

f(x) = 2x^3 - 10x^2 - 4x + 48

Step-by-step explanation:

If a cubic function has zeros a, b, c, then its equation is

f(x) = k(x - a)(x - b)(x  c)

f(x) = k(x - (-2))(x - 3)(x - 4)

f(x) = k(x + 2)(x - 3)(x - 4)

f(5) = k(5 + 2)(5 - 3)(5 - 4)

f(5) = k(7)(2)(1)

f(5) = 14k

We are told f(5) = 28, so we set 14 equal to 28 and solve for k.

14k = 28

k = 2

f(x) = 2(x + 2)(x - 3)(x - 4)

f(x) = 2x^3 - 10x^2 - 4x + 48

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: