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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

Respuesta :

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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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