Answer
(a)
f(0) = -2
f(2) = 10
f(-2) = 10
f(3) = 25
f($\sqrt 2$) = 4
f(3t) = 27t² - 2
(b)
f(0) = 0
f(2) = 4
f(-2) = -4
f(3) = 6
f($\sqrt 2$) = 2$\sqrt 2$
f(3t) = 1/3t, if t $\gt$ 1. f(3t) = 2(3t) = 6t, if t $\leq$ 1
Work Step by Step
(a)
f(0) = 3(0)² - 2 = -2
f(2) = 3(2)² - 2 = 3 $\times$ 4 - 2 = 10
f(-2) = 3(-2)² - 2 = 3 $\times$ 4 - 2 = 10
f(3) = 3(3)² - 2 = 3 $\times$ 9 - 2 = 25
f($\sqrt 2$) = 3($\sqrt2$)² - 2 = 3 $\times$ 2 - 2 = 4
f(3t) = 3(3t)² - 2 = 3 $\times$ 9t² - 2 = 27t² - 2
(b)
f(0) = 2 $\times$ 0 = 0
f(2) = 2 $\times$ 2 = 4
f(-2) = 2 $\times$ (-2) = -4
f(3) = 2 $\times$ 3 = 6
f($\sqrt 2$) = 2$\sqrt 2$
3t = 3 -> t = 1, so f(3t) = 1/3t, if t $\gt$ 1. f(3t) = 2(3t) = 6t, if t $\leq$ 1
