Question

How do you find the domain of `f(x)= (8x)/((x-1)(x-2))`?

Answer 1

`x inRR,x!=1,2`

Explanation:

`f(x)" is defined for all values of x except values which"`
`"make f(x) undefined"`

`"the denominator of f(x) cannot be zero as this would make"`
`"f(x) undefined. Equating the denominator to zero and "`
`"solving gives the values that x cannot be"`

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

`rArrx=1,x=2larrcolor(red)"are excluded values"`

`"domain is "x inRR,x!=1,2`

`(-oo,1)uu(2,+oo)larrcolor(blue)"in interval notation"`
graph{(8x)/((x-1)(x-2)) [-10, 10, -5, 5]}

Answer 2

Ask yourself where the function is defined.

Explanation:

Since the given function is a rational function, look where is the denominator is equal to zero. (`(8x)/0`is not defined)
(`x-1)(x-2)=0` if `x_1=1` or `x_2=2`
The domain of `f(x)` is : `RR-{1,2}` real number except 1 and 2