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Find the requested composition or operation.

f(x) = 8x - 5, g(x) = 2x+6
Find (fg)(x).

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Ebenezer O. | Aerospace Engr & Air Traffic Control Grad For General Ed. TutoringAerospace Engr & Air Traffic Control Gra...
4.6 4.6 (13 lesson ratings) (13)
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Given;
f(x) = 8x - 5
g(x) = 2x+6
 
(fg)(x) = f(x) * g(x)
 
(fg)(x) = (8x - 5)(2x + 6)
 
(fg)(x) = (16x2 + 48x - 10x - 30)
 
(fg)(x) = (16x2 + 38x -30)

Comments

Hi Ebenezer;
I think you accidentally multiplied 8x by 5.
Thanks Vivian...i'll correct that.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Sue;
f(x) = 8x - 5, g(x) = 2x+6
Find (fg)(x)
(fg)(x)=(8x-5)(2x+6)
Let's FOIL...
FIRST...(8x)(2x)=16x2
OUTER...(8x)(6)=48x
INNER...(-5)(2x)=-10x
LAST...(-5)(6)=-30
(fg)(x)=16x2+48x-10x-30
(fg)(x)=16x2+38x-30
This can also be written as...
(fg)(x)=2(8x2+19x-15)
Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
5.0 5.0 (229 lesson ratings) (229)
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Hi Sue,
 
f(x)=8x-5
 
g(x)=2x+6
 
(fg)(x)=f(x)g(x)
 
         =(8x-5)(2x+6)
 
         =16x²+48x-10x-30
 
         =16x²+38x-30
David T. | Experienced Math and Physics TutorExperienced Math and Physics Tutor
4.8 4.8 (12 lesson ratings) (12)
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The answer by Parviz is incorrect for the problem as written.
 
(fg)(x) uses the same assumed notation as arithmetic. Therefore, in the same spirit as my previous response,
 
(fg)(x) = (f*g)(x) = f(x)*g(x) = (8x-5)(2x+6).
 
The problem that Parviz solved was f(g(x)) which is often written (f º g)(x). Notice, in particular the open circle that separates the functions f and g. It is shorthand for " of " and thus represents putting g(x) in where ever you would normally have placed "x" in the function f. This is the procedure that Parviz demonstrated, but was not the one that was given in the request.
 
 
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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f(x) = 8x -5   g(x) = 2x +6
 
  f( g(x) )= 8( 2X +5) - 5
 
              = 16X +35