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Critical help please. Level 3 maths algebraic methods is really hard.

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

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

I need to show my working out, please help someone

  • MATHS -

    by fg I assume you mean f*g
    f*g = (x^2+3)*(2x+1) = 2x^3 + x^2 + 6x + 3

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

  • MATHS -

    Thank you steve

    It says i need to find f(g), i got a different result for some reason help please!

    And also in the second part, how did you get g^-1 = (x-1)/2

    Thank you steve x

  • MATHS -

    That's because fg is ambiguous. I did f(x) * g(x).

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

    to get g^-1, just solve for x

    g = 2x+1
    g-1 = 2x
    x = (g-1)/2
    then switch variables, and g^-1 = (x-1)/2

  • MATHS -

    Is there any reason why f(g)=g^2+3
    why do we replace the x with g?

    Sorry steve im trying my hardest to understand this

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