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)
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) $g(1-t)$
Solution
Solution Steps
To solve the given problems, we need to evaluate the function g(x)=2x2−2x+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.
Step 1: Evaluate g(0)
To find g(0), substitute x=0 into the function g(x)=2x2−2x+2:
g(0)=2(0)2−2(0)+2=2g(0)=2
Step 2: Evaluate g(−1)
To find g(−1), substitute x=−1 into the function g(x)=2x2−2x+2:
g(−1)=2(−1)2−2(−1)+2=2(1)+2+2=6g(−1)=6
Step 3: Evaluate g(4)
To find g(4), substitute x=4 into the function g(x)=2x2−2x+2:
g(4)=2(4)2−2(4)+2=2(16)−8+2=32−8+2=26g(4)=26