Given that f(x) = x^{-1} + \frac{x^{-1}}{1+x^{-2}}, what is f(f(-2))? Express your answer as a common fraction.
I think this looks a little better:
Let's first find f(-2):
we can simplify this somewhat, since the denominator in the second term is
1 + 1/4 = 5/4, and so the second term becomes - 4/10 or -2/5
f(-2) = -1/2 - 2/5 = -5/10 - 4/10 = - 9/10
Next we must find f(-9/10):
The first term evaluates to -10/9, ans so does the numerator in the second term.
The denominator is 1 + 1/(81/100), or 1 + 100/81, that is 181/81.
So the second term now evaluates to (-10/9)/(181/100) = -1,000/729
The sum of the two terms is -10/9 - 1,000/729 = -810/729 - 1,000/729 = -1,810/729 or -2 -352/729.
That is, if my calculations are correct... This was quite an excercise, so maybe I'm wrong somewhere...
I get the following:
(Check your calculation "So the second term now evaluates to (-10/9)/(181/100) = -1,000/729" tuffla2022)
Thank You, Alan. It was late, and I must have made some simple error somewhere.