Home > Math Group > Question and Answer

Math Group

Question:

pavelpimen
pavelpimen
Student
High School - 10th Grade

Find out all linear functions which are increasing and have the structure: f(f(x))=4x+3.

Rate question:

Posted by pavelpimen on Wednesday April 22, 2009 at 7:07 AM and tagged with linear function, math.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    f(f(x)) = 4x+3 given.

    To find all linear functions , f(x).

    The solution f(x) is said to be linear.

    We assume f(x) = ax+b and determine a,b.

    f(f(x)) = a*f(x)+b = a(ax+b)+b = (a^2 )x+(a+1)b

    Therefore , 4x+3  is identical to  (a^2)x+(a+1)b. Equate the coefficients of x and constant terms .

    a^2= 4=> a=+2 or a=-2

    (a+1)b=3  gives b=1 when a=2 or  b= -3 when a=-2

    Therefore, the  linear functions are  f(x) = 2x+1  or

    f(x) =-2x-3  of which    f(x) = 2x+1 is an increasing function and  the other  not.

     

     

    Rate answer:

    Posted by neela on Wednesday May 27, 2009 at 8:38 AM