Answer:
It is not a one to one function
Step-by-step explanation:
Required
Determine if f(x) = round(x) is a one to one function
This question is best answered using illustrating values;
Let x = 1.1
f(x) = round(x) becomes
f(1.1) = round(1.1)
f(1.1) = 1
Let x = 1.3
f(x) = round(x) becomes
f(1.3) = round(1.3)
f(1.3) = 1
Notice that for the two values of x, f(x) has the same value of 1.
This two illustrating values can be used to conclude that the fuction is not one-to-one.
The value of and
<u>Solution:</u>
Given, Line passes through points
Slope of line passing through two points is
Equation of a straight line passing through point-slope form is
Since we have two points we can use any point. Let us take and m and substitute in (1)
[By equating as ]
Substituting the other coordinates also gives the same result.
This question can be solved primarily by L'Hospital Rule and the Product Rule.
I) Product Rule and L'Hospital Rule:
II) Product Rule and L'Hospital Rule:
III) Product Rule and L'Hospital Rule:
IV) Product Rule and L'Hospital Rule:
V) Using the Definition of Limit:
Given:
The numbers are .
To find:
All the values that cannot be probabilities.
Solution:
We know that,
The minimum value of favorable outcomes is 0 and the maximum value is equal to the total outcomes. So, the value of probability lies between 0 and 1, inclusive. It other words, the probability lies in the interval [0,1].
From the given values only lie in the interval [0,1]. So, these values can be probabilities.
The values does not lie in the interval [0,1]. So, these values cannot be probabilities.
Therefore, the correct values are .