Proving the Range of a Polynomial Function Using Set Theory

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Homework Help Overview

The discussion revolves around proving the range of a polynomial function defined as f:ℝ→ℝ, where f(x) = x^2 + x + 2. The original poster seeks assistance in demonstrating that the range of this function is [7/4, +∞[.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the minimum value of the polynomial and question the original poster's understanding of the function's behavior. There are attempts to clarify the minimum value of related expressions and to guide the original poster in their reasoning.

Discussion Status

The discussion includes various interpretations of the polynomial's minimum value, with some participants providing insights and corrections. There is an indication that the original poster has made progress in their understanding, but no explicit consensus has been reached regarding the proof itself.

Contextual Notes

Participants are navigating through potential misunderstandings about polynomial properties and minimum values, which may affect the proof of the range. The original poster's request for a starting point suggests a need for foundational clarification.

mtayab1994
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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?
 
Last edited:
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What is the minimum value of x2+x+1?
 
the minimum value for x^2+x+1 is obviously 1
 
If x=-1/2, [itex]x^2+ x+ 1= 1/4- 1/2+ 1= 3/4[/itex]. Try thinking before reacting!
 
HallsofIvy said:
If x=-1/2, [itex]x^2+ x+ 1= 1/4- 1/2+ 1= 3/4[/itex]. 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
 

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