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Answer:
g^-1(x) = 1/(x+2)
Step-by-step explanation:
To find the inverse of the function ...
y = g(x)
swap the variables and solve for y.
x = g(y)
x = 1/y -2 . . . . . . . use the given g(x)
x +2 = 1/y . . . . . . . add 2
y(x +2) = 1 . . . . . . multiply by y
y = 1/(x +2) . . . . . divide by the coefficient of x
The inverse function is ...
[tex]\boxed{g^{-1}(x)=\dfrac{1}{x+2}}[/tex]
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Additional comment
Please observe that when the fraction is typeset, as in the boxed answer, the fraction bar serves as a grouping symbol. It shows you that the denominator is the sum x+2.
When the same expression is written in plain text, only the first item after the division symbol (/ or ÷) is considered to be in the denominator. That is, 1/x+2 = (1/x)+2. The presence or absence of a (space) has no bearing on the correct interpretation of the expression. Only parentheses will serve as a grouping symbol in plain text expressions.
g^-1(x) = 1/(x+2)
