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Z asked in Science & MathematicsMathematics · 1 decade ago

[f o g] [x] and [g o f] [x]? (Algebra 2)?

f(x)=x+5

g(x)=x^2+6

f(x)=2x

g(x)=3x-4

f(x)=x-4

g(x)=3x^2

I don't understand these. My book does a really bad job of explaining them. I remember that I have to use substitution however whenever I try to solve them that way it doesn't look right.

Thanks in advance!

*In class we do not use SIN, COS, and TAN.*

6 Answers

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  • 1 decade ago
    Favorite Answer

    PROBLEM ONE.

    f(x) = x + 5

    g(x) = x^2 + 6

    [f o g] (x) = f(g(x)) = f(x^2 + 6) = x^2 + 6 + 5 = x^2 + 11

    [g o f] (x) = g(f(x)) = g(x + 5) = (x + 5)^2 + 6 = x^2 + 10x + 25 + 6 = x^2 + 10x + 31

    PROBLEM TWO.

    f(x) = 2x

    g(x) = 3x - 4

    [f o g] (x) = f(g(x)) = f(3x - 4) = 2(3x - 4) = 6x - 8

    [g o f] (x) = g(f(x)) = g(2x) = 3(2x) - 4 = 6x - 4

    PROBLEM THREE.

    f(x) = x - 4

    g(x) = 3x^2

    [f o g] (x) = f(g(x)) = f(3x^2) = 3x^2 - 4

    [g o f] (x) = g(f(x)) = g(x - 4) = 3(x-4)^2 = 3(x^2 - 8x + 16) = 3x^2 - 24x + 48

    Note: You are not really solving anything here, you are just plugging things in in order to see what comes out. Also note that generally [f o g] (x) is not equal to [g o f] (x).

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  • 3 years ago

    Gof Algebra

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  • Shy
    Lv 6
    1 decade ago

    Hi Z

    1.

    (x)=x+5

    g(x)=x^2+6

    (fog)x = (x^2 +6) +5 = x^2+11

    (gof)x = (x+5)^2 + 6 = x^2 + 10x + 31

    2.

    f(x)=2x

    g(x)=3x-4

    (fog)x = 2(3x-4) = 6x-8

    (gof)x = 3(2x) - 4 = 6x - 4

    3.

    f(x)=x-4

    g(x)=3x^2

    (fog)x = 3x^2 - 4

    (gof)x = 3(x-4)^2 = 3x^2 - 24x + 48

    Shy

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  • Anonymous
    1 decade ago

    1) fog(x)=f(g(x)),

    let's say g(x)=x^2+6=y

    so fog(x)=f((g(x))=f(y)=y+5

    replace/substitute y=x^2+6

    to get fog(x)= x^2+6+5=x^2+11

    similarly gof(x)=g(f(x))

    f(x)= x+5=y

    resulting in gof(x)=g(y)=y^2+6 = (x+5)^2 +6

    the others can be solved similarly

    2)fog(x)=f(g(x))=f(3x-4)=2(3x-4)

    gof(x)=g(f(x))=g(2x)=3(2x)-4

    3)fog(x)=f(g(x))=f(3x^2)=3x^2-4

    gof(x)=g(f(x))=g(x-4)=3(x-4)^2

    Hope that helped

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  • 1 decade ago

    if u have (fog) put the g(x) equation in for the x in the f(x)

    x^(2)+6+5=x^(2) + 11 that would be for (fog)

    (x+5)^(2) +6= x^(2) +10x +31 (gof)

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  • 4 years ago

    those definition of purposes inform you what comes out reckoning on what is going in. So utilising f(x)= 2x+5 Then f(sin(x)) = 2*sin(x) + 5 f( f(x) ) = f( 2x + 5) = 2*( 2x + 5) + 5 f (container) = 2*container + 5 and so on. Do you notice how this works?

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