Question

PLEASE HELP ASAP
are f(x)=4/x-2-1 and g(x)=3/x+2-2 inverses of each other?​

Answer 1

To find the inverse of:

`f (x)=(4)/(x-2)-1`

Set the function to y:

`\implies y=(4)/(x-2)-1`

Rearrange to make x the subject:

`\implies y+1=(4)/(x-2)`

`\implies (y+1)(x-2)=4`

`\implies xy-2y+x-2=4`

`\implies xy+x=2y+6`

`\implies x(y+1)=2y+6`

`\implies x=(2y+6)/(y+1)`

Swap x and y:

`\implies y=(2x+6)/(x+1)`

Change y to the inverse of the function sign:

`\implies f`
`\:^(-1)(x)=(2x+6)/(x+1)`

Rewrite g(x) as a fraction:

`g(x)=(3)/(x+2)-2`

`\implies g(x)=(3)/(x+2)-(2(x+2))/(x+2)`

`\implies g(x)=(3-2(x+2))/(x+2)`

`\implies g(x)=(3-2x-4)/(x+2)`

`\implies g(x)=-(2x+1)/(x+2)`

Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other