Question

f(x) = x^2 + 1/x^2 find f (1/x)​

Answer 1

Step-by-step explanation:

Note that (x+1x)2=x2+2+1x2. Hence it looks like f(x)=x2−2 is a good candidate. Of course, ∣∣x+1x∣∣≥2 implies that we cannot say anything about f(x) if |x|<2. But for |x|≥2, we can find a real number t such that t2−xt+1=0 (and hence t+1t=x), namely t=x±x2−4√2, and then see that indeed f(x)=f(t+1t)=t2+1t2=x2−2.