Prove that the function f:[1, infinity] -- (0, infinity) defined by f(x) =1/x maps onto (0, infinity)

Question

Prove that the function f:[1, infinity] --> (0, infinity) defined by f(x) =1/x maps onto (0, infinity)

swissgirl · Answer

What is wrong with this proof?

swissgirl · Answer

Suppose $ w \in (0, \inf) $. Choose $ x= \frac{1} {x} $. Then $ f(x) = \frac{1} {\frac{1} {w}} =w $ Therefore the function f is onto (0, infinity)

anonymous · Answer

sorry i cant help :(
ask telliott99

swissgirl · Answer

hahaha alright @telliott99  can u help me?

anonymous · Answer

lol

swissgirl · Answer

Maybe all the proof is missing is that $w \neq 0 $

swissgirl · Answer

waittt a sec I messed up $ x= \frac{1} {w} $

zzr0ck3r · Answer

that is not missing, you say w is in (0,inf) thus  not 0

swissgirl · Answer

so what can be missing?

zzr0ck3r · Answer

o say that x is in the domain

zzr0ck3r · Answer

hmm if w is in (0,inf) 1/w is not always in (1,infinity)

swissgirl · Answer

ohhh so if w is a subset of (0. inf) we still must show that 1/w is a subset of (1 infinity) ok