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

In summary, the domain and range of the given functions are as follows: (a) Domain: [-2,10], Range: [5,10](b) Domain: [-2,10], Range: [14,24]
  • #1
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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  • #2
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 ?
 
  • #3
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?
 
  • #4
Do you know what is meant by domain and range? Can you define it?
Hint: Is f(24) defined?
 
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  • #5
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
 
  • #6
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.
 
  • #7
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## ...
 

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

What is a domain and range?

A domain refers to the set of all possible input values of a function, while a range refers to the set of all possible output values of a function.

How do I find the domain and range of a function?

To find the domain of a function, you can look at the given input values or find any restrictions on the input values. To find the range, you can analyze the behavior of the function and determine the output values it can produce.

Can the domain and range of a function be the same?

Yes, it is possible for the domain and range of a function to be the same. This can happen when the function is a one-to-one function, meaning each input value corresponds to a unique output value.

What happens if the domain or range of a function is not specified?

If the domain or range of a function is not specified, it is assumed to be all real numbers. However, it is important to check for any restrictions or limitations on the input or output values.

Why is it important to know the domain and range of a function?

Knowing the domain and range of a function helps us understand the behavior and limitations of the function. It also allows us to determine the possible values the function can take and helps us identify any potential errors or issues with the function.

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