SOLUTION: 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

Algebra.Com
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(52776)   (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. ".


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