# Application in Set Theory

Polynomial Function.

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?

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

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