If f(x)=1 + 1/x, prove that f(x) + f (1/x) = f (x) f (1/x)
2006-11-16 09:02:26 · 4 answers · asked by Peel I 1 in Science & Mathematics ➔ Mathematics
You know that f(x) = 1 + 1/x
f(1/x) = 1 + 1/(1/x) = 1 + x
f(x) + f(1/x) = 1 + 1/x + 1 + x
= 2 + 1/x + x
f(x) * f(1/x) = (1+ 1/x)(1+x)
= 1 + x + 1/x + 1
= 2 + 1/x + x
Thus, it has been proven.
2006-11-16 09:05:54 · answer #1 · answered by MsMath 7 · 3⤊ 3⤋
start with f(x)*f(1/x)
plug x and 1/x into f(x)=1+1/x
f(x)=1+1/x , f(1/x)=1+1/(1/x)
Plug this into the starting equation
f(x)*f(1/x)=(1+1/x)*(1+x)
=1(1+x)+1/x(1+x)
=1+x+1/x+1
=(1+x)+(1+1/x)
=f(x)+f(1/x)
2006-11-16 17:11:52 · answer #2 · answered by schizohamster 2 · 3⤊ 0⤋
substitue the functions
(1+(1/x))+f(1/x)=(1+(1/x))*f(1/x)
(1+(1/x))+(1+(1/(1/x)))=(1+(1/x))*(1+(1/(1/x)))
(1+(1/x))+(1+(x))=(1+(1/x))*(1+(x))
2+x+(1/x)=1+x+(1/x)+(x/x)
2+x+(1/x)=1+x+(1/x)+1
2+x+(1/x)=2+x+(1/x)
x+(1/x)=x+(1/x)
x=x
2006-11-16 17:09:08 · answer #3 · answered by cltcprd33 2 · 3⤊ 0⤋
i think you should figure it out yourself
2006-11-16 17:03:40 · answer #4 · answered by STORMY K 3 · 2⤊ 3⤋