SOLUTION: Could you please help me on this question? If m(x)= x+5/x-1 and n(x) = x – 3, which function has the same domain as (m of n)(x)?

Algebra ->  Functions -> SOLUTION: Could you please help me on this question? If m(x)= x+5/x-1 and n(x) = x – 3, which function has the same domain as (m of n)(x)?       Log On


   

Question 1048416: Could you please help me on this question?
If m(x)= x+5/x-1 and n(x) = x – 3, which function has the same domain as (m of n)(x)?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If m%28x%29=+%28x%2B5%29%2F%28x-1%29 and+n%28x%29+=+%28x+-3%29,
m%28x%29=+%28x%2B5%29%2F%28x-1%29-> since denominator cannot be equal to zero, exclude
x=1, so domain is { x element R: x%3C%3E1 }
+n%28x%29+=+%28x+-3%29-> since denominator cannot be equal to zero, exclude
x=3, so domain is { x element R: x%3C%3E3 }

which function has the same domain as

%28m+_of_+n%29%28x%29=m%28n%28x%29%29

m%28n%28x%29%29=m%28+%28x%2B5%29%2F%28x-1%29+%29

m%28+%28x%2B5%29%2F%28x-1%29+%29=%28x%2B5%29%2F%28x-1%29-3

m%28+%28x%2B5%29%2F%28x-1%29+%29=%28x%2B5%29%2F%28x-1%29-3%28x-1%29%2F%28x-1%29

m%28+%28x%2B5%29%2F%28x-1%29+%29=%28x%2B5%29%2F%28x-1%29-%283x-3%29%2F%28x-1%29

m%28+%28x%2B5%29%2F%28x-1%29+%29=%28x%2B5-%283x-3%29%29%2F%28x-1%29

m%28+%28x%2B5%29%2F%28x-1%29+%29=%28x%2B5-3x%2B3%29%2F%28x-1%29

m%28+%28x%2B5%29%2F%28x-1%29+%29=%28-2x%2B8%29%2F%28x-1%29

m%28+%28x%2B5%29%2F%28x-1%29+%29=-2%28x-4%29%2F%28x-1%29

and the domain is:
{ x element R: x%3C%3E1 }
so, m%28x%29 have same as domain as %28m+_of_+n%29%28x%29