Question

The picture says it all

Answer 1

Answer: Choice C)
h(x) = 11/(x-4)

-----------------------------------------------
-----------------------------------------------

Step-by-step explanation:

m(x) = (x+5)/(x-1)
n(x) = x-3
are the two given functions


`(m \circ n) (x)` is the same as m(n(x))
n(x) is the inner function
m(x) is the outer function

m(x) = (x+5)/(x-1) .... Start with m(x)
m(n(x)) = (n(x)+5)/(n(x)-1) .... Replace every x with n(x)
m(n(x)) = (x-3+5)/(x-3-1) .... Replace every n(x) on the right side with x-3
m(n(x)) = (x+2)/(x-4)

The domain of m(n(x)) is the set of real numbers x such that x can't equal 4 (to avoid dividing by zero). This is because x-4 = 0 leads to x = 4

Similarly, choice C has the same domain as it has the same denominator (x-4)

So that's why the answer is choice C