Math Problem Statement
The domain of the function f(x) is [−12,22] and the range is [−6,0]. Using interval notation, find the domain and range of g(x)=f(2x)
Solution
Given the function has a domain of and a range of , we need to find the domain and range of .
Domain of
To find the domain of , we need to determine for which -values the argument of , i.e., , lies within the domain of .
The domain of is , so we require:
Dividing through by 2:
Thus, the domain of is .
Range of
The range of is determined by the range of , because is just a horizontal scaling of by a factor of 2. Since the range of is and the transformation does not affect the output values of , the range of remains the same as that of .
Thus, the range of is .
Conclusion
- The domain of is .
- The range of is .
Would you like further details on how transformations affect functions, or do you have any other questions?
Related Questions:
- What would happen to the domain and range if ?
- How does multiplying the argument of a function by a constant affect its graph?
- If had a different domain, say , how would that change the domain of ?
- How would the domain and range of compare to ?
- What is the effect of vertical stretching on the range of a function?
Tip:
When a function is horizontally compressed (as in ), its domain shrinks, but the range remains unchanged.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Functions
Transformations
Domain and Range
Formulas
Domain of g(x) = f(2x): -12 ≤ 2x ≤ 22, Range of g(x) remains same as f(x)
Theorems
Horizontal scaling transformations
Suitable Grade Level
Grades 10-12
Related Recommendation
Finding Domain and Range for g(x) = 2f(x - 1)
Finding the Domain and Range of a Transformed Function g(x) = 2f(x + 7) - 7
Find Domain and Range of Transformed Function g(x) = f(x - 6)
Domain and Range of g(x) = f(1/4x) Given f(x) Domain and Range
Domain and Range of Transformed Functions: y = -2f(x) and y = 1/2 f(x)