Answer:
f(-3)=6 is the greatest value in the range of
for the domain (-3,0,1,2)
Step-by-step explanation:
Given that the function f is defined for range by
for the domain (-3,0,1,2)
To find the greatest value in the range of
for the domain (-3,0,1,2):
for the domain (-3,0,1,2)
That is put x=-3 in the given function
we get
![f(-3)=(-3)^2-3](https://tex.z-dn.net/?f=f%28-3%29%3D%28-3%29%5E2-3)
![=3^2-3](https://tex.z-dn.net/?f=%3D3%5E2-3)
![=9-3](https://tex.z-dn.net/?f=%3D9-3)
![=6](https://tex.z-dn.net/?f=%3D6)
Therefore f(-3)=6
put x=0 in the given function
we get
![f(0)=(0)^2-3](https://tex.z-dn.net/?f=f%280%29%3D%280%29%5E2-3)
![=0-3](https://tex.z-dn.net/?f=%3D0-3)
![=-3](https://tex.z-dn.net/?f=%3D-3)
Therefore f(0)=-3
put x=1 in the given function
we get
![f(1)=(1)^2-3](https://tex.z-dn.net/?f=f%281%29%3D%281%29%5E2-3)
![=1-3](https://tex.z-dn.net/?f=%3D1-3)
![=-2](https://tex.z-dn.net/?f=%3D-2)
Therefore f(1)=-2
put x=-3 in the given function
we get
![f(2)=(2)^2-3](https://tex.z-dn.net/?f=f%282%29%3D%282%29%5E2-3)
![=4-3](https://tex.z-dn.net/?f=%3D4-3)
![=1](https://tex.z-dn.net/?f=%3D1)
Therefore f(2)=1
Comparing the values of f(-3)=6,f(0)=-3,f(1)=-2,and f(2)=1 to find the greatest value in the range of f(x) = x^2 - 3 for the domain (-3,0,1,2) we get
Therefore f(-3)=6 is the greatest value in the range of
for the domain (-3,0,1,2)