Question 62851
QUESTION:

 Let the function f be defined by y = f(x), where x and f(x) are real numbers.  Find f(2), f(-3).

f(x) = 3/x^2+3

ANSWER:

f(x) = 3/x^2+3


To find f(2), replace x by 2 in the given function.


f(2) = 3/2^2+3

     =3/4 + 3

     = 3/4 + 3/1     ( 3 can be written as 3/1)

     = {4*3/4 + 4 * 3/1}/4 

(Multiply the whole expression with the LCD of
the denominators and put the LCD as common denominator. 4 is the least common devisor of 1 and 4)


     = {4*3/4 + 4 * 3/1}/4 



     = {1*3 + 12 }/4


     = {15}/ 4

     =15/4

Similarly,


f(-3) = 3/-3^2+3

      = 3/9 + 3

      = 1/3 + 3/1

      = {3*1/3 + 3* 3/1}/3

      = { 1 + 9 }/3

      =  10/3


If your question is f(x) = 3/(x^2+3)


f(2) = 3/(2^2+3)

     = 3 /(4 +3)

     = 3/7

f(-3) = 3/(-3^2+3)

      = 3 / ( 9 + 3)

      = 3 / 12
     
      = 1/4



Regards.

praseenakos@yahoo.co.in