Domain of g(x): [-1,2) | Calc Homework Question

  • Thread starter Thread starter George3
  • Start date Start date
  • Tags Tags
    Domain
AI Thread Summary
To find the domain of g(x) = f(2x + 3) given f(x) has a domain of [-1, 5), the transformation of the function needs to be analyzed. Setting the inequalities for the domain of f, we solve for x in the equations 2x + 3 = -1 and 2x + 3 = 5. This leads to the values of x that correspond to the endpoints of the domain of f, resulting in the domain of g(x) being [-1, 2). The calculations confirm that the transformed values fall within the original domain of f. Thus, the domain of g(x) is correctly identified as [-1, 2).
George3
Messages
31
Reaction score
0

Homework Statement


I have a review in Calc and the question was:
f(x) has a domain of [-1 , 5) Find the domain of g(x) = f(2x+3)



Homework Equations





The Attempt at a Solution


I got [-1 , 2)
 
Physics news on Phys.org
If x=-1, then 2x+3=_______?
If x=2, then 2x+3=________?

Does that agree with the domain of f?
 
For what value of x is 2x+ 3= -1? For what value of x is 2x+ 3= 5?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Find the domain and the range of ##f-3g##
Replies
3
Views
1K
What is the domain of f(f(x)) for f(x)= x/(1+x)?
Replies
3
Views
1K
What are the implied domain and range of cos(arctan(x))?
Replies
3
Views
2K
Finding the domain of a composite function
Replies
10
Views
2K
Finding the domain (and range) of a logarithmic function
Replies
11
Views
3K
How to identify the type of function?
Replies
23
Views
3K
To find the range of a given ##\sin## function
Replies
15
Views
2K
How to find the range of a function with square roots?
Replies
23
Views
2K
What is the domain of a trig function with y = 2sin(x)?
Replies
3
Views
1K
Composite and Inverse Functions Problem
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top