Find the Domain and Range of Functions with Given Domain and Range Values

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Homework Help Overview

The discussion revolves around finding the domain and range of functions derived from a given function f, which has a specified domain of [-2,10] and range of [5,10]. The specific transformations being considered are f(2x+4) and 2f(x)+4.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the implications of substituting values from the original domain and range into the transformed functions. There are questions regarding the definitions of domain and range, as well as the validity of certain input values.

Discussion Status

Some participants are attempting to clarify their understanding of domain and range, while others are questioning the assumptions made about the transformations. There is an ongoing exploration of how to apply the given domain and range to the new functions.

Contextual Notes

There are indications of confusion regarding the definitions of domain and range, as well as the notation used to express them. Some participants are also questioning whether certain values are defined within the context of the function.

Mark53
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Homework Statement


Suppose f is a function with domain [-2,10] and range [5,10]. Find the domain and range of the following functions.
(a) f(2x+4)

(b) 2f(x)+4

The Attempt at a Solution


[/B]
Would I just substitute the in the domain and range values to find the answer?
 
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Don't ask. Do it: that counts as an attempt at solution. Ask when stuck...
Or (in a friendlier manner :smile:) what do you get when you do as you propose ?
 
BvU said:
Don't ask. Do it: that counts as an attempt at solution. Ask when stuck...
Or (in a friendlier manner :smile:) what do you get when you do as you propose ?
[-2,10] if i sub this values into f(2x+4) i would get 0 and 24 does this mean that the domain would be (0,24)

Would I just do the same for the range?
 
Do you know what is meant by domain and range? Can you define it?
Hint: Is f(24) defined?
 
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fresh_42 said:
Do you know what is meant by domain and range? Can you define it?
Hint: Is f(24) defined?
the domain is pairs of x coordinates in order and the range is pairs of y coordinates in order
 
Mark53 said:
the domain is pairs of x coordinates in order and the range is pairs of y coordinates in order
The domain of a function is the set of values which are allowed to be used as inputs to the function. The notation "[-2,10]" denotes a range of values from -2 up through 10, inclusive. It does not denote an ordered pair.
 
Remember that ##f(2x+4)=f\circ g## where ##g(x)=2x+4##, the composition requires that the range of ##g## is included in the domain of ##f## ...
 

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