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

AI Thread Summary
The discussion focuses on finding the domain and range of functions derived from a given function f with a domain of [-2,10] and a range of [5,10]. For the function f(2x+4), the transformation affects the input values, leading to a new domain that needs careful evaluation to ensure it falls within the original domain of f. The range of the transformed function must also be calculated based on the output values from the original range. The conversation emphasizes understanding the definitions of domain and range, as well as the importance of ensuring that the outputs of one function fit within the inputs of another. Overall, the key takeaway is the necessity of applying transformations correctly while adhering to the constraints of the original 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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