Proving the Range of a Polynomial Function Using Set Theory

[mtayab1994]

Polynomial Function.

Homework Statement

f:ℝ→ℝ
x→x^2+x+2

Homework Equations

Prove that: f(ℝ)=[7/4,+∞[

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?

 

[daveb]

What is the minimum value of x²+x+1?

 

[mtayab1994]

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

 

[HallsofIvy]

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

 

[mtayab1994]

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

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