Question

`\begin{gathered}f(x) = (5)/(x - 4) \: \: \: g(x) (6)/(x) \: \: \: \\\end{gathered}`find f°g(x).

Answer 1

Given

`f(x)=(5)/(x-4),\text{ }g(x)=(6)/(x)`

To find:

`f\circ g(x)`

Step-by-step explanation:

It is given that,

`f(x)=(5)/(x-4),\text{ }g(x)=(6)/(x)`

That implies,

`\begin{gathered} f\circ g(x)=f(g(x)) \\ =f((6)/(x)) \\ =(5)/((6)/(x)-4) \\ =(5)/((6-4x)/(x)) \\ =(5x)/(6-4x) \\ =(5x)/(2(3-2x)) \end{gathered}`

Hence, the value is,

`f\circ g(x)=(5x)/(2(3-2x))`

And, the domain is,

`\begin{gathered} 6-4x=0 \\ 4x=6 \\ x=(6)/(4) \\ x=(3)/(2) \end{gathered}`

Therefore, the domain is,

`Domain:(-\infty,(3)/(2))\cup((3)/(2),\infty)`