Question

Please help I need to clarify if the questions are correct I don't really know the domain though

Answer 1

`Domain\text{ of goh: (-}\infty,\text{ 2) }\cup\text{ (2, }\infty)`

Step-by-step explanation:

(g o h)(x): inserting the values of h(x) into g(x)

g(x) = (x + 6)/(x+ 5)

h(x) = 2x - 9

`\begin{gathered} \mleft(goh\mright)\mleft(x\mright)=\frac{(2x\text{ -9)+6}}{(2x\text{ -9)+5}} \\ =\text{ }\frac{2x\text{ -9+6}}{2x\text{ -9+5}} \\ (goh)(x)=(2x-3)/(2x-4) \end{gathered}`

To get the domain of (g o h)(x) = (2x - 3)/(2x -4)

if the value of x = 2

(g o h)(x) = (2x - 3)/(2(2) -4) = (2(2)- 3)/(4-4)

= (4-3)/0 = undefined

This means the domain of x is from negative infinty to number before 2. And from number after 2 to positive infinity. 2 makes it undefined.

In interval notation:

Since 2 is not inclusive, it would have ) instead of ]

`Domain\text{ of goh: (-}\infty,\text{ 2) }\cup\text{ (2, }\infty)`