Question

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

Answer 1

Answer:

Step-by-step explanation:

m (x) = (x+ 5) / (x -1)        and     n(x) = x - 3.

$m(x) = \dfrac{x+5}{x-1}$

Hence

$m(n) = \dfrac{n+5}{n-1}$

but n is a function and n = x-3. Now, replace value of n on m (n)

$(m(n))= \dfrac{(x-3)+5}{(x-3)-1}$

simplify it

$(m\bullet n)(x) =\dfrac{x+2}{x-4}$

since (m . n) (x)  is a fraction function, its domain will be all x such that the denominator is NOT 0. That is

$x-4\ne 0\rightarrow x\ne 4$

among options, only C has the same denominator with $(m\bullet n)(x)$

Hence their domains are the same.