If `f(x)=(4x+3)/(6x-4),\ x\ !=2/3,` show that `fof(x)=x` for all `x!=2/3dot` What is the inverse of `f?`

Explanation

We have` f(x)=frac{4 x+3}{6 x-4}, x ne frac{2}{3} `
`
therefore f circ f(x)=f(f(x))=f(frac{4 x+3}{6 x-4}) `
`
=frac{4(frac{4 x+3}{6 x-4})+3}{6(frac{4 x+3}{6 x-4})-4}=frac{16 x+12+18 x-12}{24 x+18-24 x+16}=frac{34 x}{34}=x`


for inverse of F,

take `y=frac{4 x+3}{6 x-4}`
`
therefore 6 x y-4 y=4 x+3 Rightarrow 6 x y-4 x=3+4 y`
`
x(6 y-4)=3+4 y Rightarrow x=frac{4 y+3}{6 y-4}`
`
...