The answer is f(k - 2) = 3k² - 12k + 10
The function is: f(t)=3t² - 2
We need to find f(k - 2). Since t = k - 2, we will just substitute t in the function:
t = k - 2
f(t) = 3t² - 2
f(k - 2) = 3(k - 2)² - 2 =
= 3(k² - 2 * k * 2 + 2²) - 2 =
= 3(k² - 4k + 4) - 2 =
= 3k² - 3*4k + 3*4 - 2 =
= 3k² - 12k + 12 - 2 =
= 3k² - 12k + 10