Let F(x)= x+2/x+9 Find F^-1(-10)

Answer 1

Assuming you mean y = (x+2)/(x+9)

x = (y+2)/(y+9)

x(y+9) = y+2

x(y+9) - y = 2

xy - y + 9x = 2

xy - y = 2 - 9x

y(x-1) = 2 - 9x

y = (2- 9x)/(x-1)

Finv(-10) = (2 + 90)/(-10-1) = 92/-11

Note that f( -92/11) = [ -92/11 + 22/11] / [ -92/11 + 99/11]

= -70/11 / 7/11

= -10