Find the inverse of the following function:
g(x)=1/x (space) -2

I already know the answer is 1/x+2
I just need help on how to get to that answer
PLEASE SHOW ALL WORK!!
I WILL GIVE BRAINLIEST!!

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  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 ...

_____

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)

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step-by-step explanation: