SOLUTION: Find the inverse of {{{f(x)=2/x}}}

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Question 113795: Find the inverse of f%28x%29=2%2Fx
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=2%2Fx Start with the given function


x=2%2Ff%28x%29 Switch the variables x and f(x)


Now let's solve for f(x)


x%2Af%28x%29=2 Multiply both sides by f(x)


f%28x%29=2%2Fx Divide both sides by x to solve for f(x)


Now this may seem a bit odd, but the inverse of f%28x%29=2%2Fx is itself: f%28x%29=2%2Fx


If we graph f%28x%29=2%2Fx, we get


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cx%2C+2%2Fx%29+ note: the red line should be a dotted line


and we can see that if we reflect the curve over the red line we'll get the same line (in other words the curve folds over
itself). So this visually verifies our answer