f(x)=I3x^2-6I
I'm supposed to write it as a piece wise function. help?
I'm supposed to write it as a piece wise function. help?
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solve 3x^2 - 6 = 0
3x^2 = 6
x^2 = 2
x = √2 or x = -√2
If x < -√2, then 3x^2 - 6 > 0.
If -√2 < x < √2, then 3x^2 - 6 < 0.
If x > √2, then 3x^2 - 6 > 0.
Therefore, f(x) =
{ 3x^2 - 6 if x ≤ -√2 or x ≥ √2
-(3x^2 - 6) if -√2 < x < √2 }
3x^2 = 6
x^2 = 2
x = √2 or x = -√2
If x < -√2, then 3x^2 - 6 > 0.
If -√2 < x < √2, then 3x^2 - 6 < 0.
If x > √2, then 3x^2 - 6 > 0.
Therefore, f(x) =
{ 3x^2 - 6 if x ≤ -√2 or x ≥ √2
-(3x^2 - 6) if -√2 < x < √2 }
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Just choose some points. For x=1, f(x) is 3. For x=0, f(x) would be 6. Just negate all the - signs when you're done plugging in x.
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Hints:
| g(x) | = g(x) when g(x) ≥ 0
| g(x) | = -g(x) when g(x) < 0
| g(x) | = g(x) when g(x) ≥ 0
| g(x) | = -g(x) when g(x) < 0