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A stone is dropped in a lake 2015-02-14
From Wendy:

Hi, I have problems solving this problem. We didn't exactly go over these kind of problems and the book doesn't have an example either. Thank you for your help!

A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 80 cm/s.
(a) Find a function g that models the radius as a function of time t.

g(t) =

(b) Find a function f that models the area of the circle as a function of the radius r.

f(r) =

(c) Find f compose g.
f compose g =

Answered by Penny Nom.
Composition functions 2007-06-12
From Gilligan:
Find functions f and g so that f(g(x)) = H.
(1) H(x) = (1 + x^2)^(3/2)
(2) H(x) = int(x^2 + 1)
I don't know where to start.

Answered by Stephen La Rocque.
Composition of functions 2002-04-06
From Yvonne:
In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = -x2 - 4 and g(x) = sqrt(x)

The range of f(x), x<=-4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(-x2 - 4).

In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything?

Answered by Claude Tardif.



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