How do I find the domain of K(x) = x(32 - 2x)^2?
the domain is all real numbers, -inf to +inf
your function is just a polynomial.
The domain of all polynomials is (-∞,∞)
To find the domain of the function K(x) = x(32 - 2x)^2, we need to determine the values of x for which the function is defined.
In this case, the only thing that could possibly make the function undefined is division by zero. So, we need to identify any values of x that would result in division by zero when plugging them into the function.
To do this, we set the denominator of the function equal to zero and solve for x. In this case, the denominator is (32 - 2x)^2.
(32 - 2x)^2 = 0
To solve this, we take the square root of both sides and solve for x:
32 - 2x = 0 or 32 - 2x = -0
Solving these equations, we find:
32 - 2x = 0
-2x = -32
x = 16
32 - 2x = -0
-2x = -32
x = 16
So, x = 16 is the only value that makes the function undefined. Therefore, the domain of the function is all real numbers except x = 16.