Question
Mathematics
If the function $f\left(x\right)=2{x}^{2}+x-3$f(x)=2x^(2)+x-3, and $G\left(x\right)=\frac{2x-1}{3}$G(x)=(2x-1)/(3). find the following function values.
1. $f\left(0\right)$f(0)
2. $f\left(-2\right)$f(-2)
3. $f\left(a+5\right)$f(a+5)
4. $G\left(0\right)$G(0)
5. $G\left(-7\right)$G(-7)
6. $G\left(\frac{7}{2}\right)$G((7)/(2))
Solve problem with AI
1. $f\left(0\right)$f(0):
$f\left(0\right)=2\left(0{\right)}^{2}+0-3=-3$f(0)=2(0)^(2)+0-3=-3
2. $f\left(-2\right)$f(-2):
$f\left(-2\right)=2\left(-2{\right)}^{2}+\left(-2\right)-3=5$f(-2)=2(-2)^(2)+(-2)-3=5
3. $f\left(a+5\right)$f(a+5):
$f\left(a+5\right)=2\left(a+5{\right)}^{2}+\left(a+5\right)-3=2{a}^{2}+21a+52$f(a+5)=2(a+5)^(2)+(a+5)-3=2a^(2)+21 a+52
4. $G\left(0\right)$G(0):
$G\left(0\right)=\frac{2\left(0\right)-1}{3}=-\frac{1}{3}$G(0)=(2(0)-1)/(3)=-(1)/(3)
5. $G\left(-7\right)$G(-7):
$G\left(-7\right)=\frac{2\left(-7\right)-1}{3}=-\frac{15}{3}=-5$G(-7)=(2(-7)-1)/(3)=-(15)/(3)=-5
6. $G\left(\frac{7}{2}\right)$G((7)/(2)):
$G\left(\frac{7}{2}\right)=\frac{2\left(\frac{7}{2}\right)-1}{3}=\frac{6}{3}=2$G((7)/(2))=(2((7)/(2))-1)/(3)=(6)/(3)=2
Explanation:
7. To find $f\left(0\right)$f(0), we simply substitute 0 for x in the function $f\left(x\right)$f(x) and simplify.
8. To find $f\left(-2\right)$f(-2), we substitute -2 for x in the function $f\left(x\right)$f(x) and simplify.
9. To find $f\left(a+5\right)$f(a+5), we substitute (a+5) for x in the function $f\left(x\right)$f(x) and simplify.
10. To find $G\left(0\right)$G(0), we substitute 0 for x in the function $G\left(x\right)$G(x) and simplify.
11. To find $G\left(-7\right)$G(-7), we substitute -7 for x in the function $G\left(x\right)$G(x) and simplify.
12. To find $G\left(\frac{7}{2}\right)$G((7)/(2)), we substitute $\frac{7}{2}$(7)/(2) for x in the function $G\left(x\right)$G(x) and simplify.
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