f(x)= 2x+7/x+1 . what is the inverse of this function?

[tex]f(x) = \dfrac{2x+7}{x+1} [/tex]

[tex]\text {Let y = }f(x),[/tex]

[tex]y= \dfrac{2x+7}{x+1}[/tex]

[tex]y(x + 1) = 2x + 7[/tex]

[tex]xy + y = 2x + 7[/tex]

[tex]xy - 2x = 7 - y[/tex]

[tex]x(y - 2) = 7 - y[/tex]

[tex]x = \dfrac{7-y}{y-2} [/tex]

[tex]f^{-1}(x) = \dfrac{7-x}{x-2}[/tex]