functions and relations

Anonymous
timer Asked: Sep 16th, 2014
account_balance_wallet $5

Question Description

1) Find f(g(x)) if f(x) = 3x + 1 and g(x) = x2 - 1.

2) Find g(f(x)) if f(x) = 2x – 3 and g(x) = x2 - 1.

3)Find the zeros of f(x) = 

4) Find the zeros of f(x) = 

Tutor Answer

Ileana P
School: UIUC

1) Replace x= x^2 - 1 in f(x)

f(g(x)) = f(x^2 - 1) = 3 ((x^2)-1) + 1

                             = 3 x^2 -3 + 1  distributing 3 inside the parenthesis

                             = 3 x^2 - 2  

2) Replace x= 2x-3 in g(x)

 g(f(x) = g(2x-3) = (2x-3)^2 - 1

                          = (2x)^2 - 2(2x)(3) + 3^2 - 1       because (ax-b)^2 = a^2x^2 - 2 abx + b^2

                          = 4 x^2 - 12x + 9  - 1

                           = 4 x^2 - 12x + 8           you can divide by 4 to simplify

                           = x^2 - 3x + 2

3) Zeros of a function f(x) = 0 but you need to know the function.

   Ex: f(x)  = 3x + 1 = 0

                    3x +1 -1 = 0 - 1

                             3x = -1     then dividing by 3 both sides

                                x= -1/3  is the zero of the function 

  Ex: f(x) = 2x - 3 = 0

                   2x - 3 + 3 = 0 + 3   

                              2x = 3          then dividing by 2

                                x = 3/2  is the zero of the function.

flag Report DMCA
Review

Anonymous
Top quality work from this guy! I'll be back!

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors