Given the function:
Determine for which values of X the following holds:
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Given the function:
Determine for which values of X the following holds:
To solve this problem, we begin by analyzing the function .
The expression inside the square, , can take any real value depending on . However, when squared , it becomes non-negative for all real , meaning it is always greater than or equal to zero.
Since is defined as the negative of this square——the function is always less than or equal to zero. In other words, for all real values of .
Therefore, there are no values of that make , as the function outputs non-positive values exclusively.
Thus, the solution to the problem is No x.
No x
The graph of the function below intersects the X-axis at points A and B.
The vertex of the parabola is marked at point C.
Find all values of \( x \) where \( f\left(x\right) > 0 \).
Because any squared expression is non-negative, and when you put a negative sign in front, it becomes non-positive. So always!
Great thinking! When , we get . At this point, the function equals zero, but we need greater than zero.
No mistake! This is a valid mathematical scenario. Some inequalities have no solution, just like some equations have no solution. It's an important concept to understand.
Look for patterns like negative times squared expressions or absolute values less than negative numbers. These create impossible conditions that no real number can satisfy.
'No solution' means no x works for the inequality. 'All real numbers' means every x works. They're opposite situations - be careful not to confuse them!
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