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How do i find the inverse of this function?
f(x)=x+(1/x)
When I flip the x and y I get x=y+(1/y)
I start out by multiplying by y to get xy=(y^2)+1
But after that it gets complicated and I don't know how to get all the y's together.
Can someone please help me?
1 Answer
- 10 years ago
This one is a little tricky. I'll try to explain it as best as I can.
x=y+1/y (flip the x and y)
xy=y^2+1 (multiply by y)
xy-y^2-1=0 (move the y^2+1 over)
y^2-xy+1=0 (multiply by -1 so the y^2 is positive. See where this is going?)
y^2-xy=-1 (move the 1 over)
y^2-xy+x^2/4=-1+x^2/4
(y-x/2)^2=x^2/4-1 (factor the left side)
(y-x/2)^2=1/4(x^2-4) (factor 1/4 from the right side)
+-(y-x/2)=1/2√(x^2-4) (take the square root of both sides)
+-(y-x/2)=√(x^2-4)/2 (multiply the 1/2 in)
y-x/2=+-√(x^2-4)/2 (move the +- over)
y=(√(x^2-4))+x)/2 or (x-√(x^2-4))/2
A very confusing answer I know but the trick to solving it is completing the square with only variables.
Source(s): School
