Question

F(x)= (x-7)
-----
(2x+5)

find F^-1 (x)

Answer 1

To find the inverse switch the x and y from you original function\[y=\frac{x-7}{2x+5}\]
switch the x with y and find y:\[x=\frac{y-7}{2y+5}\rightarrow (2y+5)x=y-7\rightarrow 2yx+5x=y-7\]
\[5x+7=y-2yx\]
fractor out a y form the right hand side:\[5x+7=(1-2x)y \rightarrow y=\frac{5x+7}{1-2x}\]

Answer 2

so is my answer Y=

Answer 3

sorry I should have changed it its\[f^{-1}(x)=\frac{5x+7}{1-2x}\]

Answer 4

Thank you very much.