Question

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

Answer 1

What is wrong with this proof?

Answer 2

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)

Answer 3

sorry i cant help :(
ask telliott99

Answer 4

hahaha alright @telliott99 can u help me?

Answer 5

lol

Answer 6

Maybe all the proof is missing is that \(w \neq 0 \)

Answer 7

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

Answer 8

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

Answer 9

so what can be missing?

Answer 10

o say that x is in the domain

Answer 11

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

Answer 12

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