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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

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abidemiokin

Answer:

[tex]g^{-1}x = \frac{1-2x}{x}[/tex]

Step-by-step explanation:

Given the function [tex]g(x)= \frac{1}{x+2}[/tex], we are to find the inverse of the function and this can be done y following the simple steps:

Step 1: Replace y with [tex]g(x)[/tex]

[tex]g(x)= \frac{1}{x+2}\\y= \frac{1}{x+2}[/tex]

Step 2: Interchange x with y

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

Step 3: Make y the subject of the formula;

[tex]x= \frac{1}{y+2}\\y+2 = \frac{1}{x}\\y = \frac{1}{x} - 2\\Find \ the\ LCM\\y = \frac{1-2x}{x}[/tex]

Step 4: Replace y as [tex]g^{-1}(x)[/tex]

[tex]g^{-1}x = \frac{1-2x}{x}[/tex]

Hence the inverse of the function is [tex]g^{-1}x = \frac{1-2x}{x}[/tex]

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