Prove that f(x) = 3*x + 11 is uniformly continuous

[squaremeplz]

Homework Statement

Prove that f(x) = 3*x + 11 is uniformly continuous.

Homework Equations

x,y in S and |x-y| < a imply |f(x)-f(y)| < e

The Attempt at a Solution

following the book I get to

f(x) - f(y) = 3(x-y)

i just don't know how to chose e in this case..

would it be |f(x) - f(y)| < e/3

any pointers are greatly appreciated

 

[Mark44]

The idea is that you can make f(a) arbitrarily close to f(b) by specifying how close a must be to b, regardless of where a and b are.

So if you wanted f(a) to be within 0.03 of f(b), how close must a be to b?

 

[icantadd]

Homework Statement

i just don't know how to chose e in this case..

would it be |f(x) - f(y)| < e/3

any pointers are greatly appreciated

You already did, you just forgot to say that the proof was done. By the time you get to | f(x) - f(y) | = | 3(x-y) | then look, you know you can make (x-y) smaller than some d, how small? Smaller than e/3. Then it follows that for e>0
if |(x-y)| < d = (e/3) then |3(x-y)| < 3*(e/3) = e