Question

X+ 5If m(x)=X-1 and n(x) = x - 3, which function has the same domain as (mon(x)?X+5O h(x) =1111Oh(x) =X-1h(x)=11X-411Oh(x)=X-3

Answer 1

We have to first find the compound function:

`\begin{gathered} (m\circ n)(x)=m(n(x))=(n(x)+5)/(n(x)-1) \\ (n(x)+5)/(n(x)-1)=((x-3)+5)/((x-3)-1)=(x+2)/(x-4) \\ \Rightarrow(m\circ n)(x)=(x+2)/(x-4) \end{gathered}`

The domain of this compound function is all the real values but x=4, where the function has a discontinuity.

Then, any function that has a domain of "all real values but x=4" will have the same domain as our compound function.

This is the case for h(x)=11/(x-4), because it also has one discontinuity at x=4.

Answer: Third option, h(x)=11/(x-4)