Answer:
Domain of the function is Option 1. (-∞,1)∪(1,∞).
Step-by-step 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)) = [tex]\frac{(\frac{x-1}{x}-1) }{2(\frac{x-1}{x})} \\[/tex]
Now we multiply numerator and denominator by x.
fФ(g(x) = [tex]\frac{x-1-x}{2(x-1)}[/tex]
= [tex]-\frac{1}{2}(\frac{1}{x-1})[/tex]
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).
