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    hi

    I have a few questions and don't know where to start

    1) express 2sinx + 4cosx in the form Rsin(x + a)

    2) given f(x) = 2x^3 and g(x)=3x + 1

    Evaluate fg(-2)
    Find g^(-1)x
    State the value of gg^(-1)k
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    1) I'm pretty sure that A = 45

    Let me know if that's right, then i'll write out the workig including R.
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    1) expand Rsin(x+a) by using compound angle formulae.
    Spoiler:
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     Rsinxcosa + Rsinacosx


    the equate coefficients of  sin x and  cos x

    Spoiler:
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     Rcosa =  2

     Rsina = 4


    can you eliminate R to find a? can you eliminate a to find R?

    Spoiler:
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     \frac{Rsina}{Rcosa} = \frac{2}{4}

    and

    R^2cos^2a = 4

    R^2sin^2a = 16

    therefore  R^2(cos^2a + sin^2a) = 20

    NB  cos^2a + sin^2a =?


    then rewrite Rsin(x+a) having found R and a....
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    2)
    can you find fg(x)?
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    2(3x+1)^3


    then substitute x=-2 into fg(x)

    to find g^{-1}(x) say y=3x+1, make x the subject, and then replace y with x, and x with g^{-1}(x)
    Spoiler:
    Show
     g^{-1}(x) = \frac{x-1}{3}


    if you dont see what  gg^{-1}(x) is right away, try figuring it out in the same way you found fg(x).
 
 
 
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