The mapping diagram shows a functional relationship
1 answer:
Answer:
f(x) = 4 when x is 8
Step-by-step explanation:
Domain is the set of x values that make the function defined. Allowed x values for the function (mapping).
The Range is the set of y values that make the function defined. Allowed y values for the function (mapping).
- Whenever we need to find f(a), suppose, then we look for "a" in the domain and see its corresponding value mapping in the range.
- Whenever we will be given a value for f(x) = a, suppose, and we have to find "x", we look at the value a in the range and find corresponding x value in the domain.
Firstly, we need f(4), so we look for "4" in domain and see which number it corresponds to in range.
That is
Thus,
Next,
We want "x" value that gives us a "y" value of 4. We look for "4" in the range and see which value it corresponds to. That is "8". So,
f(8) = 4
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The rational number that lies exactly halfway between a/b and c/d on a number line is x = (ad + bc)/2bd or 1/2(a/b + c/d).
<h3>How to calculate the mid-value?</h3>To calculate the mid-value of two numbers x and y, find the average of these two numbers. I.e., (x + y)/2
Thus, the average of these two numbers is the mid-value between them.
<h3>Calculation:</h3>It is given that,
a/b and c/d are the two rational numbers on a number line.
Consider the required rational number that lies exactly halfway between a/b and c/d as 'x'.
Then, the mid-value of these two rational numbers is
(a/b + c/d)/2
⇒ (ad + bc)/2bd ...(i)
To know that the obtained rational number is exactly halfway between a/b and c/d, consider the distance from a/b to x and c/d to x.
So, the distance from a/b to x is - "x - a/b" (x > a/b) and
the distance from x to c/d is - "c/d - x"
From the given condition, the above-obtained distances are equal
⇒ x - a/b = c/d - x
⇒ x + x = a/b + c/d
⇒ 2x = (ad + bc)/bd
⇒ x = (ad + bc)/2bd ...(ii)
From (i) and (ii), it is concluded that the required rational number is
x = (ad + bc)/2bd
Learn more about finding mid-value between two rational numbers here:
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Disclaimer: The given question on the portal was incomplete. Here is the complete question.
Question: CHALLENGE: Let a/b and c/d be two distinct rational numbers. Find the rational number that lies exactly halfway between a/b and c/d on a number line.
