Question

What is the greatest value in the range of f(x) = x^2 - 3 for the domain (-3,0,1,2)

Answer 1

f(-3)=6 is the greatest value in the range of
`f(x)=x^2-3` for the domain (-3,0,1,2)

Explanation:

Given that the function f is defined for range by
`f(x)=x^2-3` for the domain (-3,0,1,2)

To find the greatest value in the range of
`f(x)=x^2-3` for the domain (-3,0,1,2):

`f(x)=x^2-3` for the domain (-3,0,1,2)

That is put x=-3 in the given function
`f(x)=x^2-3` we get

`f(-3)=(-3)^2-3`

`=3^2-3`

`=9-3`

`=6`

Therefore f(-3)=6

put x=0 in the given function
`f(x)=x^2-3` we get

`f(0)=(0)^2-3`

`=0-3`

`=-3`

Therefore f(0)=-3

put x=1 in the given function
`f(x)=x^2-3` we get

`f(1)=(1)^2-3`

`=1-3`

`=-2`

Therefore f(1)=-2

put x=-3 in the given function
`f(x)=x^2-3` we get

`f(2)=(2)^2-3`

`=4-3`

`=1`

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
`f(x)=x^2-3` for the domain (-3,0,1,2)