Question

Find the domain of the function:

Answer 1

Option C is correct.

Explanation:

We have given the function.

f(x) = (x-1)²/(x³-2x²+x)

We have to find the domain of given function.

domain of function is all possible values of independent variable for which the function is difined.

So for this the denominator must not be zero.

x³-2x²+x ≠ 0

x(x²-2x+1)≠ 0

x(x-1)(x-1) ≠ 0

x ≠0 and x≠1

So, the domain cannot consist of x=0 and x=1.

Therefore, the domain is :

(-∞ , 0) ∪ (0,1 ) ∪ (1,+∞).

Answer 2

Answer: OPTION C.

Explanation:

1. The domain of the function given in the problem are all those values for which the function that is in the denomiantor is different from zero, because the division by 0 is not allowed.

2. You can make the denominator equal to zero and solve it, as you can see below:

`x^(3)-2x^(2)+x=0\\x(x^(2)-2x+1)=0\\x(x-1)(x-1)=0\\x=0\\x=1`

3. Therefore, the domain is:

(-∞,0)U(0,1)U(1,∞)