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)

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)
Transcript text: Given that $\mathrm{g}(\mathrm{x})=2 \mathrm{x}^{2}-2 \mathrm{x}+2$, find each of the following. a) $g(0)$ b) $g(-1)$ c) $g(4)$ d) $g(-x)$ e) $g(1-t)$
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Solution

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Solution Steps

To solve the given problems, we need to evaluate the function g(x)=2x22x+2 g(x) = 2x^2 - 2x + 2 at specific values of x x .

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

Step 1: Evaluate g(0) g(0)

To find g(0) g(0) , substitute x=0 x = 0 into the function g(x)=2x22x+2 g(x) = 2x^2 - 2x + 2 : g(0)=2(0)22(0)+2=2 g(0) = 2(0)^2 - 2(0) + 2 = 2 g(0)=2 \boxed{g(0) = 2}

Step 2: Evaluate g(1) g(-1)

To find g(1) g(-1) , substitute x=1 x = -1 into the function g(x)=2x22x+2 g(x) = 2x^2 - 2x + 2 : g(1)=2(1)22(1)+2=2(1)+2+2=6 g(-1) = 2(-1)^2 - 2(-1) + 2 = 2(1) + 2 + 2 = 6 g(1)=6 \boxed{g(-1) = 6}

Step 3: Evaluate g(4) g(4)

To find g(4) g(4) , substitute x=4 x = 4 into the function g(x)=2x22x+2 g(x) = 2x^2 - 2x + 2 : g(4)=2(4)22(4)+2=2(16)8+2=328+2=26 g(4) = 2(4)^2 - 2(4) + 2 = 2(16) - 8 + 2 = 32 - 8 + 2 = 26 g(4)=26 \boxed{g(4) = 26}

Final Answer

g(0)=2 \boxed{g(0) = 2}

g(1)=6 \boxed{g(-1) = 6}

g(4)=26 \boxed{g(4) = 26}

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