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Answer:
The statement that best describes the domain and range of p(x) and q(x) is:
p(x) and q(x) have the same domain and the same range.
Step-by-step explanation:
We are given a function p(x) as:
[tex]p(x)=6-x[/tex]
AS the function is a polynomial function.
Hence it is defined everywhere for all the real values.
Hence, the domain of the function p(x) is: All Real numbers.
and the range of the function p(x) is: All the real numbers.
and the function q(x) is given by:
[tex]q(x)=6x[/tex]
which is also a polynomial function.
Hence, it also has the same domain and range.
Domain and range are specific sets for each function. For given case, p(x) and q(x) have the same domain and range.
What is domain and range of a function?
Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
The domain and range of given functions are:
- p(x) = 6-x
For any real number value of x, p(x) just takes 6-x(negates the input and add 6 to it), thus, its always defined, and thus, its domain is all real numbers.
Since p = 6-x is possible to go negatively infinite and positively infinite and always continuous, thus, its range is all real numbers(all numbers are possible as its output)
We can prove the above statement. Let some real number T is not in the range of p(x). But we have T = 6-x => x = 6-T which is a real number, thus, for input 6-T, there is output T. Thus, its a contradiction, and thus, all real numbers are in range of p(x).
Thus,
- Range of p(x): [tex]x \in \mathbb R[/tex] (R is all real numbers' set)
- Domain of p(x): [tex]x \in \mathbb R[/tex]
- q(x) = 6x
Its scaling all numbers. All numbers can be multiplied by 6 and produce a valid result. Thus, its domain is all real numbers.
Suppose that we've T as a real number. Then we can get this as output if we put input as x = T/6 (since then 6x = 6(T/6) = T)
Thus, all real numbers are in its output set, thus, its range is all real numbers.
The Range of q(x): [tex]x \in \mathbb R[/tex] and Domain of q(x): [tex]x \in \mathbb R[/tex]
Hence, for given case, p(x) and q(x) have the same domain and range.
Learn more about domain and range here:
https://brainly.com/question/26077568
