Let f(x) = 16 - x^2, g(x) = 4 - x. Find (fg)(x) and its domain.

Mathematics

1 answer:

timofeeve [1]3 years ago

5 0

Answer:

(fg)(x) = x^3-4x^2-16x+64, D: All Real Numbers

Step-by-step explanation:

(fg)(x) = f(x) x g(x)

= 16-x^2(4-x)

=64-16x-4x+x^3

(fg)(x) = x^3-4x^2-16x+64

Domain is all real numbers because you can substitute any real number for x and the function would still work.

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<u>Geometric Sequences</u>

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

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It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

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