|
Question 1142447: Suppose the functions f and g are defined by
f(x) = x^2(x + 1) (x − 2) and g (x) = x^2
Which of the following statements is / are true?
A. f (−1) = 0
B. g (x + 1) = x^2 + 1
C. (f/g)(x) = (x + 1) (x − 2) and Df/g = R
1. Only A
2. Only B
3. Only C
4. Only A and B
5. A, B and C
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = x^2 * (x + 1) * (x - 2)
f(-1) = (-1)^2 * (-1 + 1) * (-1 - 2) = 1 * 0 * -3 = 0
statement A is true.
g(x) = x^2
g(x+1) = (x+1)^2 = x^2 + 2x + 1
statement B is false.
(f/g)(x) = f(x) / g(x) = x^2 * (x + 1) * (x - 1) / x^2 = (x + 1) * (x - 1)
that part of statement C is true, i think.
i don't understand what you mean by Df/g = R
there is a box in the beginning of your statement C that doesn't mean anything to me.
Answer by ikleyn(52754)  (Show Source):
You can put this solution on YOUR website! .
(A) f(-1) = 0 by substitution.
So, statement A is TRUE.
(B) This statement is FALSE, obviously.
(C) (f/g)(x) = (x+1)(x-2) everywhere, except the point / (the points) where g(x) = 0,
BY THE DEFINITION of what is the ratio of two functions.
Df/g is, BY THE CONTEXT, the domain of the function (f/g)(x), and this domain is R \ {0} : the set of all real numbers
except of 0 (except of zero)
So, the statement (C) is FALSE.
The ANSWER to the problem's question / (questions) is " 1. Only A. ".
|
|
|
| |
