Given the function f(x) = -0.5|2x + 2| + 1, for what values of x is f(x) = 6?
1 answer:
Answer:
<em>No values of x can make f(x)=6</em>
Step-by-step explanation:
Equation with Absolute Value
The absolute value of a number is always positive. That condition must be met when solving equations. Any condition that goes against the rule, must be discarded and not part of the solution.
The function provided in the question is:
We need to find the value(s) of x that make:
f(x)=6
It needs to solve the equation:
Subtracting 1:
Dividing by -0.5:
We reach to this equation to solve:
As stated above, the absolute value is always positive, and the equation forces the absolute value to be negative. There is no possible value of x that makes the absolute value negative, thus:
No values of x can make f(x)=6
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General Idea:
Domain of a function means the values of x which will give a DEFINED output for the function.
Applying the concept:
Given that the x represent the time in seconds, f(x) represent the height of food packet.
Time cannot be a negative value, so
The height of the food packet cannot be a negative value, so
We need to replace for f(x) in the above inequality to find the domain.
The possible solutions of the above inequality are given by the intervals . We need to pick test point from each possible solution interval and check whether that test point make the inequality
true. Only the test point from the solution interval [-200, 200] make the inequality true.
The values of x which will make the above inequality TRUE is
But we already know x should be positive, because time cannot be negative.
Conclusion:
Domain of the given function is
Answer: 9
Step-by-step explanation:
Use Pythagorean's Theorem for a right triangle.