Question

This is factor by grouping. did I do 1a right and how do I continue on 1b

Answer 1

We will have the following:

*First: ( f ° g) (x):

`(f\circ g)(x)=(((1)/(x))+1)/(((1)/(x))-2)\Rightarrow(f\circ g)(x)=(((1+x)/(x)))/(((1-2x)/(x)))`
`\Rightarrow(f\circ g)(x)=((1+x)(x))/((x)(1-2x))\Rightarrow(f\circ g)(x)=(1+x)/(1-2x)`

Domain:

`(-\infty,(1)/(2))\cup((1)/(2),\infty)`

*Second: (f ° f) (x):

`(f\circ f)(x)=(((x+1)/(x-2))+1)/(((x+1)/(x-2))-2)\Rightarrow(f\circ f)(x)=((((x+1)+(x-2))/(x-2)))/((((x+1)-2(x-2))/(x-2)))`
`\Rightarrow(f\circ f)(x)=(((2x-1)/(x-2)))/(((-x+5)/(x-2)))\Rightarrow(f\circ f)(x)=((2x-1)(x-2))/((x-2)(-x+5))`
`\Rightarrow(f\circ f)(x)=(2x-1)/(-x+5)`

Domain:

`(-\infty,5)\cup(5,\infty)`