- #1

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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?

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- Thread starter mtayab1994
- Start date

- #1

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f:ℝ→ℝ

x→x^2+x+2

Prove that: f(ℝ)=[7/4,+∞[

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

Last edited:

- #2

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What is the minimum value of x^{2}+x+1?

- #3

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

- #4

HallsofIvy

Science Advisor

Homework Helper

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

- #5

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If x=-1/2, [itex]x^2+ x+ 1= 1/4- 1/2+ 1= 3/4[/itex]. Trythinkingbefore 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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