*f(x)=x+2 g(x)=4x*

^{2}-10*Find (FoG)(x) and (GoF)(x)*

^{2}-10)+2 = 4x

^{2}-8 Replace the x+2 with g(x)+2

^{2}-10 = 4x

^{2}+16x+6 Replace the x in 4x

^{2}-10 with with 4(f(x))

^{2}-10

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

(FoG)(x)

(GoF)(x)

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

(fog)(x) = (4x^{2}-10)+2 = 4x^{2}-8 Replace the x+2 with g(x)+2

(gof)(x) = 4(x+2)^{2}-10 = 4x^{2}+16x+6 Replace the x in 4x^{2}-10 with with 4(f(x))^{2}-10

To solve (FoG)(x), everywhere you see the value **x** in the function f(x) substitute the value of g(x) [in this case, 4x^{2}-10], so in this case:

(FoG)(x) = (4x^{2}-10)+2

= 4x^{2}-10+2

= 4x^{2}-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)

= 4(x

= 4x

Chen Jang T. | MaCT (Math and Chemistry Tutor)MaCT (Math and Chemistry Tutor)

(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

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