Question

Given: f(n) = 2n – 2 and g(n) = 2n+5
Find:
(f•g)(t-1)

Answer 1

(f · g)(t - 1) = 4t² - 2t - 13

Explanation:

First, find (f · g)(n). You can do this by multiplying f(n) by g(n).

f(n) = 2n - 2

g(n) = 2n + 5

(f · g)(n) = (2n - 2)(2n + 5)

(f · g)(n) = 4n² + 6n - 10

Now, plug (t - 1) into (f · g)(n) and simplify.

(f · g)(n) = 4n² + 6n - 10

(f · g)(t - 1) = 4(t - 1)² + 6(t - 1) - 10

(f · g)(t - 1) = 4(t² - 2t + 1) + 6(t - 1) - 10

(f · g)(t - 1) = 4t² - 8t + 4 + 6t - 1 - 10

(f · g)(t - 1) = 4t² - 8t + 4 + 6t - 1 - 10

(f · g)(t - 1) = 4t² - 2t + 4 - 1 - 10

(f · g)(t - 1) = 4t² - 2t - 13