chris215
  • chris215
Find the range for f(x) = x2 + 1, for x < 0. y ≥ 1 y > 1 y < 1 y ≤ 1 A?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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freckles
  • freckles
\[x<0 \\ \text{ multiply } x \text{ on both sides } x \cdot x >0 \cdot x \\ \text{ do you know why I change the direction of the inequality ? }\]
freckles
  • freckles
hint: what does x<0 mean in words
chris215
  • chris215
x less than 0?

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freckles
  • freckles
or x is negative if you multiply both sides of an inequality by a negative number you have to change the direction of the inequality
freckles
  • freckles
\[x<0 \\ x \cdot x> 0 \cdot x \\ x^2 >0 \\ \text{ now add 1 on both sides } x^2+1>0+1\]
freckles
  • freckles
\[x^2+1>1 \]
freckles
  • freckles
remember x^2+1 is y since we had f(x)=x^2+1
chris215
  • chris215
ohh ok thank you!
freckles
  • freckles
np

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