# Homework Help: Application in Set Theory

1. Oct 25, 2011

### mtayab1994

Polynomial Function.

1. The problem statement, all variables and given/known data

f:ℝ→ℝ
x→x^2+x+2

2. Relevant equations

Prove that: f(ℝ)=[7/4,+∞[

3. The attempt at a solution

Well I don't know how answer this, so can someone give me a clue on how to start it off?

Last edited: Oct 25, 2011
2. Oct 25, 2011

### daveb

What is the minimum value of x2+x+1?

3. Oct 25, 2011

### mtayab1994

the minimum value for x^2+x+1 is obviously 1

4. Oct 25, 2011

### HallsofIvy

If x=-1/2, $x^2+ x+ 1= 1/4- 1/2+ 1= 3/4$. Try thinking before reacting!

5. Oct 26, 2011

### mtayab1994

Yea thanks for the tip i already tried it out yesterday and i figured it out.

Once i stated that x=-1/2 then i get x^+x+2=7/4