Answer:
Range = (-∞,0) U (0,∞)
Explanation:
The given function is:
f(x) = (x-1)²/x³-2x²+x
We can reduce the denominator:
= (x-1)²/x(x²-2x+1)
we know that a²-2ab+b² = (a-b)²
= (x-1)²/x(x-1)²
= 1/x
The function 1/x is undefined for x = 0.
Hence, its domain lies in (-∞,0) U (0,∞).
Hence x can either be less than or greater than zero.
The function f(x) is greater than zero when x<0.
The function f(x) is less than zero when x>0.
There is no way the function can be zero because the numerator is constant.
Hence the domain of the function lies in the interval:
(-∞,0) U (0,∞)