Domain of the composition of these functions

AI Thread Summary
The composition of the functions f, g, and h results in f(g(h(x))) = 4x^2 - 1. The domain of this composition is all real numbers. Participants confirm the correctness of the solution and inquire about the range and the graph's characteristics. The discussion highlights the importance of understanding both the domain and the graphical behavior of the resulting function. Overall, the focus remains on the composition's domain and its implications for further analysis.
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Homework Statement



Form the composition f o g o h and give the domain.
f(x) = x - 1, g(x) = 4x, h(x) = x2

Homework Equations





The Attempt at a Solution



f(g(h(x))) = 4x2-1

The domain of x is any real number.
 
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your answer looks to be correct.
 
Looks good to me.

You know how to state the range as well?
 
What is the shape of the graph? Does it have a maximum or minimum?
 

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