Answer:
f(-3)=6 is the greatest value in the range of [tex]f(x)=x^2-3[/tex] for the domain (-3,0,1,2)
Step-by-step explanation:
Given that the function f is defined for range by [tex]f(x)=x^2-3[/tex] for the domain (-3,0,1,2)
To find the greatest value in the range of [tex]f(x)=x^2-3[/tex] for the domain (-3,0,1,2):
[tex]f(x)=x^2-3[/tex] for the domain (-3,0,1,2)
That is put x=-3 in the given function [tex]f(x)=x^2-3[/tex] we get
[tex]f(-3)=(-3)^2-3[/tex]
[tex]=3^2-3[/tex]
[tex]=9-3[/tex]
[tex]=6[/tex]
Therefore f(-3)=6
put x=0 in the given function [tex]f(x)=x^2-3[/tex] we get
[tex]f(0)=(0)^2-3[/tex]
[tex]=0-3[/tex]
[tex]=-3[/tex]
Therefore f(0)=-3
put x=1 in the given function [tex]f(x)=x^2-3[/tex] we get
[tex]f(1)=(1)^2-3[/tex]
[tex]=1-3[/tex]
[tex]=-2[/tex]
Therefore f(1)=-2
put x=-3 in the given function [tex]f(x)=x^2-3[/tex] we get
[tex]f(2)=(2)^2-3[/tex]
[tex]=4-3[/tex]
[tex]=1[/tex]
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 [tex]f(x)=x^2-3[/tex] for the domain (-3,0,1,2)
