Answer:
Explanation:
To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:
a) g(0)
To find g(0), substitute x = 0 into the function:
g(0) = 2(0)^2 - 2(0) + 9
g(0) = 0 - 0 + 9
g(0) = 9
b) g(-1)
To find g(-1), substitute x = -1 into the function:
g(-1) = 2(-1)^2 - 2(-1) + 9
g(-1) = 2(1) + 2 + 9
g(-1) = 2 + 2 + 9
g(-1) = 13
c) g(2)
To find g(2), substitute x = 2 into the function:
g(2) = 2(2)^2 - 2(2) + 9
g(2) = 2(4) - 4 + 9
g(2) = 8 - 4 + 9
g(2) = 13
d) g(-x)
To find g(-x), substitute x = -x into the function:
g(-x) = 2(-x)^2 - 2(-x) + 9
g(-x) = 2x^2 + 2x + 9
e) g(1 - t)
To find g(1 - t), substitute x = 1 - t into the function:
g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9
g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9
g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9
g(1 - t) = 2t^2 - 2t + 9
Therefore:
a) g(0) = 9
b) g(-1) = 13
c) g(2) = 13
d) g(-x) = 2x^2 + 2x + 9
e) g(1 - t) = 2t^2 - 2t + 9