Search 74,072 tutors
FIND TUTORS
Ask a question
0 0

Given functions f and g, perform the indicated operations:

Tutors, please sign in to answer this question.

5 Answers

(a ± b)2 = a2 ± 2ab + b2  
(f o g)(x) = f(g(x))
~~~~~~~~~~~~~~ 

f(x) = 8x2 - 7x
g(x) = 8x - 4

(f o g)(x) = f[g(x)] =

8(8x - 4)2 - 7(8x - 4) =

8(64x2 - 64x + 16) - 56x + 28 =

512x2 - 512x + 128 - 56x + 28 =

512x2 - 568x + 156
I'm sorry, Kateln, I'm sort of in the fog on this one.  I'm not sure what (fog)(x) means, but I'm going to interpret if as f[g(x)]
 
f of g of x
 
f[g(x)] = 8*[g(x)]2 - 7*{g(x)]
 
= 8*(8x - 4)2 - 7*(8x - 4)
 
= 512x2 -512x + 128 - (56x - 28)
 
= 512x2 - x(512 + 56) + 156
 
= 512x2 - 568x + 156
 
= 128x2 - 142 + 39
 
I hope I've interpreted the problem correctly.

Comments

(f o g)(x) = 4(128x^2 - 142x + 39)
William, the composite function is not an equation, and you changed it completely by dividing each coefficient by 4. If you applied distributive property, you have to keep "4" outside the parentheses.
(fog)(x) is the standard notation for functional composition.  It is the name of the function whose values are f(g(x)).
f(x)=8x^2-7x
g(x)=8x-4
f(g(x))=f(8x-4)=8(8x-4)^2-7(8x-4)
                      =8(64x^2-64x+16)-56x+28
                      =512x^2-512x+128-56x+28
                      =512x^2-568x+156

Woodbridge Algebra tutors