Questions: Given that g(x)=2x^2-2x+2, find each of the following. a) g(0) b) g(-1) c) g(4) d) g(-x) e) g(1-t)

Solution Steps

To solve the given problems, we need to evaluate the function $g(x) = 2x^2 - 2x + 2$ at specific values of $x$.

a) For $g(0)$, substitute $x = 0$ into the function. b) For $g(-1)$, substitute $x = -1$ into the function. c) For $g(4)$, substitute $x = 4$ into the function.

To find $g(0)$, substitute $x = 0$ into the function $g(x) = 2x^2 - 2x + 2$: $$g(0) = 2(0)^2 - 2(0) + 2 = 2$$ $$\boxed{g(0) = 2}$$

To find $g(-1)$, substitute $x = -1$ into the function $g(x) = 2x^2 - 2x + 2$: $$g(-1) = 2(-1)^2 - 2(-1) + 2 = 2(1) + 2 + 2 = 6$$ $$\boxed{g(-1) = 6}$$

To find $g(4)$, substitute $x = 4$ into the function $g(x) = 2x^2 - 2x + 2$: $$g(4) = 2(4)^2 - 2(4) + 2 = 2(16) - 8 + 2 = 32 - 8 + 2 = 26$$ $$\boxed{g(4) = 26}$$

Final Answer