Question

Inverse equation: `f^-1(x)=(-11x-1)/(-7x+3)` were `x!=3/7`, what would the domain be?

Answer 1

`D_f=x in RR, x!=3/7`

Explanation:

`f^-1(x)=(-11x-1)/(-7x+3)`

Apart from `x!=3/7`, there are no other values for which `f^-1` is undefined, thus `x` can take all real values barring `3"/"7`.
graph{(-11x-1)/(-7x+3) [-10, 10, -5, 5]}

You can see this from the graph where `f^-1` has only one asymptote at `x=3"/"7`

Answer 2

`x inRR,x!=3/7`

Explanation:

`" the domain is all real values apart from any that make the"`
`"denominator zero which make the function undefined"`

`"equating the denominator to zero and solving gives the "`
`"value that x cannot be"`

`"solve " -7x+3=0rArrx=3/7larrcolor(red)" excluded value"`

`rArr"domain is " x inRR,x!=3/7`