Question

If f(x) = 2x - 4 and g(x) = x² - 4x, find the value of g[f(k+1)].

a) 4k² - 4k - 4
b) 2k² - 4k + 4
c) k² - 4k - 2
d) 2k² - 2k - 4

Answer 1

The value of g[f(k+1)] is 4k² - 4k - 4.

Step-by-step explanation:

The first step is to find the value of f(k+1):

f(k+1) = 2(k+1) - 4

f(k+1) = 2k + 2 - 4

f(k+1) = 2k - 2

Next, substitute this value into g(x):

g[f(k+1)] = (2k - 2)² - 4(2k - 2)

g[f(k+1)] = (2k - 2)(2k - 2) - 4(2k - 2)

g[f(k+1)] = 4k² - 4k - 4

Therefore, the value of g[f(k+1)] is 4k² - 4k - 4.