Problem
Given that \( g(x)=3 x^{2}-4 x+6 \), find each of the following. a) \( g(0) \) b) \( g(-2) \) c) \( g(2) \) d) \( g(-x) \) e) \( g(1-t) \) a) \( g(0)=6 \) (Simplify your answer.) b) \( g(-2)=26 \) (Simplify your answer.) c) \( g(2)=10 \) (Simplify your answer.) d) \( g(-x)= \) (Simplify your answer.)
Solution
Step 1 ：a) \( g(0)=3(0)^{2}-4(0)+6=6 \)
Step 2 ：b) \( g(-2)=3(-2)^{2}-4(-2)+6=26 \)
Step 3 ：c) \( g(2)=3(2)^{2}-4(2)+6=10 \)
Step 4 ：d) \( g(-x)=3(-x)^{2}-4(-x)+6=3x^{2}+4x+6\)
Step 5 ：e) \( g(1-t)=3(1-t)^{2}-4(1-t)+6=3(1-2t+t^{2})-4+4t+6=3t^{2}-8t+9 \)
