Could somebody help me with this please? i forgot how to do these.
1 answer:
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Answer:
The correct option is;
Step-by-step explanation:
The given information is that m(x) = x² - 17·x
The above equation can be written in the form;
y = x² - 17·x
Therefore;
0 = x² - 17·x - y
From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;
By comparison to the equation,0 = x² - 17·x - y, we have;
a = 1, b = -17, and c = -y
Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;
Which can be simplified as follows;
And further simplified as follows;
Interchanging x and y in the function of the inverse, m⁻¹(x), we have;
We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;
m'(x) = 2·x - 17 = 0
x = 17/2
Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;
m''(x) = 2 > 0, therefore, the point is a minimum point on the graph
Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;
to increase m⁻¹(x) above the minimum.
Answer:
Yes; there is only one range value for each domain value
Step-by-step explanation:
A relation can be defined as a function f(x) if for each value of the domain of x, there exists a unique value of f(x).
For example
(2, 4)(3, 9)(-2, 4)(4, 16) Is a Function
(2, 4)(2,6)(3, 8)(3, -8) Is Not a Function
To analyze if the relationship shown is a function, you must observe that each value of the domain has a single value of the range assigned.
For the given points {(-5, 6), (-2, 3), (3, 2), (6, 4)} this requirement is satisfied. Therefore, the relationship is a function. The graph is shown in the attached image.
The correct option is: Yes; there is only one range value for each domain value
