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

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