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New Gcse Maths Hard question watch

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    I'm struggling answering a question about function notation in the new Gcse papers. Here is the question:

    f(x)=2x+c
    g(x)=cx+5
    fg(x)=6x+d
    c and d are constants
    workout the value of d

    any help will be appreciated
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    (Original post by theBranicAc)
    I'm struggling answering a question about function notation in the new Gcse papers. Here is the question:

    f(x)=2x+c
    g(x)=cx+5
    fg(x)=6x+d
    c and d are constants
    workout the value of d

    any help will be appreciated
    Zacken can help. :yep:
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    (Original post by theBranicAc)
    I'm struggling answering a question about function notation in the new Gcse papers. Here is the question:

    f(x)=2x+c
    g(x)=cx+5
    fg(x)=6x+d
    c and d are constants
    workout the value of d

    any help will be appreciated
    What is f(g(x))? It is f(cx + 5) = 2(cx+5) + c = 2cx + 10 + c

    But we know that f(g(x)) = 6x + d so it must be the case that 2cx + 10 + c = 6x + d

    And hence: 2c = 6 and 10 + c = d. You can find the value of c from the first equation and hence the value of d from the second.
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    (Original post by TheOtherSide.)
    Zacken can help. :yep:
    Thanks.
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    (Original post by Zacken)
    What is f(g(x))? It is f(cx + 5) = 2(cx+5) + c = 2cx + 10 + c

    But we know that f(g(x)) = 6x + d so it must be the case that 2cx + 10 + c = 6x + d

    And hence: 2c = 6 and 10 + c = d. You can find the value of c from the first equation and hence the value of d from the second.
    I understand everything up onto the 2c = 6 part. How did you go from 2cx + 10 + c = 6x + d to 2c = 6?

    And also solving c, you get c = 3 therefore d = 13.
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    What exam board are you taking?
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    (Original post by theBranicAc)
    I understand everything up onto the 2c = 6 part. How did you go from 2cx + 10 + c = 6x + d to 2c = 6?

    And also solving c, you get c = 3 therefore d = 13.
    You compared the coefficients of x on both sides of the equation. They need to be equal for the equality to hold.
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    (Original post by Zacken)
    You compared the coefficients of x on both sides of the equation. They need to be equal for the equality to hold.
    I'm sorry but I still do not understand? I can see the coefficients of x are 2 and 6 but how does that lead to 2c = 6?
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    (Original post by theBranicAc)
    I understand everything up onto the 2c = 6 part. How did you go from 2cx + 10 + c = 6x + d to 2c = 6?

    And also solving c, you get c = 3 therefore d = 13.
    For the left hand side to be exactly the same as the right hand side, 2c must be equal to 6, as the coefficients of the x term must be same on both sides of equation.
 
 
 

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