Question

Which equation is the inverse of f(x)=LaTeX: \frac{1}{x+2}1 x + 2 A. LaTeX: f^{-1}\left(x\right)=\frac{1}{x}+2f − 1 ( x ) = 1 x + 2 B. LaTeX: f^{-1}\left(x\right)=\frac{1}{x}-2f − 1 ( x ) = 1 x − 2 C. LaTeX: f^{-1}\left(x\right)=2-\frac{1}{x}f − 1 ( x ) = 2 − 1 x D. LaTeX: f^{-1}\left(x\right)=-2-\frac{1}{x}f − 1 ( x ) = − 2 − 1 x

Answer 1

`g^(-1)x = (1-2x)/(x)`

Explanation:

Given the function
`g(x)= (1)/(x+2)`, we are to find the inverse of the function and this can be done y following the simple steps:

Step 1: Replace y with
`g(x)`

`g(x)= (1)/(x+2)\\y= (1)/(x+2)`

Step 2: Interchange x with y

`x= (1)/(y+2)`

Step 3: Make y the subject of the formula;

`x= (1)/(y+2)\\y+2 = (1)/(x)\\y = (1)/(x) - 2\\Find \ the\ LCM\\y = (1-2x)/(x)`

Step 4: Replace y as
`g^(-1)(x)`

`g^(-1)x = (1-2x)/(x)`

Hence the inverse of the function is
`g^(-1)x = (1-2x)/(x)`