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12 September, 06:32

Let f (x) = x³-27 and let g (x) = x-3. Match the functions defined below with the letters labeling their equivalent expressions.

1. g (f (x))

2. f (x2)

3. f (g (x))

4. (f (x)) 2

A. - 30 + x³

B. - 54 + 27x - 9x² + x³

C. 729 - 54x³ + x6

D. - 27 + x6

+2
Answers (1)
  1. 12 September, 06:42
    0
    1. g (f (x)) = g (x^3 - 27) (x)

    =x^3 - 27 - 3

    =x^3 - 30

    Matched with letter A.

    2. f (x^2 (x)) = (x^3 - 27) ^2

    = (x^3 - 27) (x^3 - 27)

    =x^6 - 54x^3 + 729

    Matched with letter C

    3. f (g (x)) = f (x - 3) (x)

    = (x - 3) ^3 - 27

    =[ (x - 3) (x - 3) (x - 3) ]-27

    =x^3 - 9^2 + 27x - 54

    Matched with letter B.

    4. (f (x)) 2 = (x^3 - 27) ^2

    = (x^3 - 27) (x^3 - 27)

    =x^6 - 54x^3 + 729

    Matched with letter C
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