Question

What are the possible values of x for the following functions?

f(x)= 3x/(x−1)(x−2)

Answer 1

all real numbers except the number 2 and number 1

Explanation:

we have

`f(x)=(3x)/((x-1)(x-2))`

we know that

In a quotient, the denominator cannot be equal to zero

so

`(x-1)(x-2)=0`

Solve for x

The values of x are

x=2, x=1

so

The domain of the function is all real numbers except the number 2 and number 1

In interval notation

(-∞,1) ∩ (1,2) ∩ (2,∞)