Question

Determine the domain of the function.

Answer 1

Domain of the function is Option 1. (-∞,1)∪(1,∞).

Explanation:

In the question two functions have been given as

f(x) = (x-1)/2x and g(x) = (x-1)/x

Now we have to find a function defined as (f Ф g(x))

We put the value of g(x) in f(x) to find a new function defined as fФ(g(x))

⇒ fФ(g(x)) =
`(((x-1)/(x)-1) )/(2((x-1)/(x))) \\`

Now we multiply numerator and denominator by x.

fФ(g(x) =
`(x-1-x)/(2(x-1))`

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

The function is defined only if (x-1)>0 ⇒ x >1

and (x-1)<0 ⇒ x <1

So the domain will be the combined set of ( 1,∞) and (-∞,1) or (1,∞)∪(-∞,1).