Maths

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Thanks steve for a brilliant answer! Got one last one which is gobbledegook to me.

Two functions f and g are defined by
f:x(arrow)x^2 + 3
g:x(arrow)2x + 1

find:
a) the function fg
b)solve the equation f(x) = 12g^-1(x)

Many Thanks!!!!

  • Maths -

    using the usual notation,

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

    fg = f(x)*g(x) = (x^2+3)(2x+1) = 2x^3 + x^2 + 6x + 3

    f(x) = 12g^-1(x)
    g^-1(x) = (x-1)/2
    so, solve x^2+3 = 12(x-1)/2
    x^2+3 = 6x-6
    x^2 - 6x + 9 = 0
    (x-3)^2 = 0
    x = 3

  • Maths -

    If by fg you meant f◦g (that is, f(g(x))), then

    since f(x) = x^2+3,
    f(g) = g^2+3 = (2x+1)^2+3 = 4x^2 + 4x + 4

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