What is the domain and range of # f(x) = x / (3x(x-1))#?

1 Answer
Jan 13, 2018

Answer:

Domain f(x): #{x epsilon RR | x != 0, 1}#

Explanation:

In order to determine the domain, we need to see which part of the function restricts the domain. In a fraction, it is the denominator. In a square root function, it is what's inside the square root.

Hence, in our case, it is #3x(x-1)#.

In a fraction, the denominator can never be equal to 0 (which is why the denominator is the restricting part of the function).

So, we set:
#3x(x-1) != 0#

The above means that:
#3x!= 0# AND #(x-1) !=0#

Which gives us:
#x !=0# AND #x !=1#

Thus, the domain of the function is all real numbers, EXCEPT #x = 0# and #x = 1#.

In order words, domain f(x): #{x epsilon RR | x != 0, 1}#