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# algebra help

f(x)=x+2 g(x)=4x^2-10
(FoG)(x)
(GoF)(x)

### 3 Answers by Expert Tutors

Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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f(x)=x+2   g(x)=4x2-10
Find (FoG)(x) and (GoF)(x)

The notation (fog)(x) refers to a composite function.  Basically, you just replace the x in f(x) with g(x)

(fog)(x) = (4x2-10)+2 = 4x2-8                 Replace the x+2 with g(x)+2

(gof)(x) = 4(x+2)2-10 = 4x2+16x+6        Replace the x in 4x2-10 with with 4(f(x))2-10
Rob D. | Math & Business Tutor (Not taking new clients at this time)Math & Business Tutor (Not taking new cl...
5.0 5.0 (12 lesson ratings) (12)
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To solve (FoG)(x), everywhere you see the value x in the function f(x) substitute the value of g(x) [in this case, 4x2-10], so in this case:

(FoG)(x) = (4x2-10)+2
=   4x2-10+2
=   4x2-8

Likewise, to solve (GoF)(x), everywhere you see the value x in the function g(x) substitute the value of f(x) [in this case, x+2], so in this case:

(GoF)(x) = 4(x+2)2-10
= 4(x2+4x+4)-10
= 4x2+16x+6
Chen Jang T. | MaCT (Math and Chemistry Tutor)MaCT (Math and Chemistry Tutor)
4.9 4.9 (46 lesson ratings) (46)
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(f o g)(x)=f(g(x))
= f(4x^2-10)
= (4x^2 - 10) + 2
= 4x^2 -8

(g o f)(x) = g(f(x))
= g(x+2)
= 4(x+2)^2 - 10
= 4(x^2+4x+4) - 10
= 4x^2 + 16x + 16 - 10
= 4x^2 + 16x + 6