Given functions f and g, perform the indicated operations:

Question

f(x) = 8x² -7x

g(x) = 8x - 4

 

(fog)(x)

 

I would really appreciate the steps and final outcome of this problem. Thank you!

Answer 1

N.B. Understanding composition of functions is fundamental to understanding and using the chain rule of differentiation in calculus.

Answer 2

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.

Answer 3

(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

Answer 4

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

Answer 5

f(x)=8x²-7x    g(x)=8x-4

(fog)(x)=f(g(x))=8(g(x)²)-7g(x)=8(8x-4)²-7(8x-4)=8(64x²-64x+16)-56x+28=512x²-512x+128-56x+28

=512x²-568x+156