Question

If m(x) =x+5/x-1 and n(x) = x - 3, which function has the same domain as (mºn)(x)?

Answer 1

We have

M(X) = (X + 5)/(X - 1)

N(X) = X - 3

So,

M(N(X)) =  [(X - 3) + 5]/[(X - 3) - 1]

M(N(X)) =  [X + 2]/[X - 4]

The M(N(X)) domain will be:

D = {X / X ≠ 4}

4 ∉ to the M(N(X)) domain, otherwise we would have a/0, which is not possible (a denominator with zero). An equivalent function would be

H(X) = 1/(X - 4)