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Given functions f and g, perform the indicated operations:

f(x) = 8x2 -7x
g(x) = 8x - 4
 
(fog)(x)
 
I would really appreciate the steps and final outcome of this problem. Thank you!

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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N.B. Understanding composition of functions is fundamental to understanding and using the chain rule of differentiation in calculus.
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
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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)).
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
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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
Michael F. | Mathematics TutorMathematics Tutor
4.6 4.6 (5 lesson ratings) (5)
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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
Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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(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