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18 May, 06:37

For all values of x

(2)

f (x) = (x + 2) 2 and g (x) = 3 (x - 1)

a) Find gf (x), giving your answer in the form a (x2 + bx + c)

where a, b and care integers.

(x² +

x +

b) Find g ' (12)

(2)

+4
Answers (1)
  1. 18 May, 07:06
    0
    A.) gf (x) = 3x^2 + 12x + 9

    B.) g' (x) = 2

    Step-by-step explanation:

    A.) The two given functions are:

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

    Open the bracket of the two functions

    f (x) = (x + 2) ^2

    f (x) = x^2 + 2x + 2x + 4

    f (x) = x^2 + 4x + 4

    and

    g (x) = 3 (x - 1)

    g (x) = 3x - 3

    To find gf (x), substitute f (x) for x in g (x)

    gf (x) = 3 (x^2 + 4x + 4) - 3

    gf (x) = 3x^2 + 12x + 12 - 3

    gf (x) = 3x^2 + 12x + 9

    Where

    a = 3, b = 12, c = 9

    B.) To find g ' (12), you must first find the inverse function of g (x) that is g' (x)

    To find g' (x), let g (x) be equal to y. Then, interchange y and x for each other and make y the subject of formula

    Y = 3x + 3

    X = 3y + 3

    Make y the subject of formula

    3y = x - 3

    Y = x/3 - 3/3

    Y = x/3 - 1

    Therefore, g' (x) = x/3 - 1

    For g' (12), substitute 12 for x in g' (x)

    g' (x) = 12/4 - 1

    g' (x) = 3 - 1

    g' (x) = 2.
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