Question

f(x)=1+X的平方÷1-X的平方 求证f(x分之一)=负f(x)

Answer 1

f(x)=(1+x²)/(1-x²)

证：f(1/x)=(1+1/x²)/(1-1/x²)

=[(x²+1)/x²]/[(x²-1)/x²]

=(x²+1)/(x²-1)

=-f(x)