how do you get the inverse of this function?
f(x)= 1/x+2

Question

owlfred · Answer

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anonymous · Answer

Set $$x = \frac{1}{y+2} $$ and solve for y

anonymous · Answer

get $$xy + 2x = 1$$

anonymous · Answer

so $$y = \frac{1-2x}{x} = \frac{1}{x} - 2 $$

anonymous · Answer

that is the inverse function

anonymous · Answer

but how do you simplify the 1/y+2? sorry, i'm so bad at math.

anonymous · Answer

Well, the original function was $$\frac{1}{x+2}$$ If you take the reciprocal of this you get $$x+2$$ then if you subtract 2 you get $$x$$, which is the identity function

anonymous · Answer

so the inverse function is "take reciprocal and subtract 2"

anonymous · Answer

that is , $$ \frac{1}{x} - 2$$

anonymous · Answer

ah that makes complete sense. thanks so much!!!

anonymous · Answer

No problem :) good luck with the rest of your work

anonymous · Answer

oh thansk! actually, one last question; when solving for inverses what are the usual steps you take? do you just switch x and y and simplify from there or...?