Question

Use the given domain to find the range of the function: f(x)=−x3+x2+5, D={−2, −1, 2}

Answer 1

The range of the function is
`R=\{17, 5, 1\}`.

Explanation:

Let
`f(x) = -x^(3)+x^(2)+5`. From Function Theory we must remember that the range of function corresponds to the set of images associated to each elemenf from domain. In this case, the function has a domain composed of three elements and we need to find the image of each element:

x = -2

`f(-2) = -(-2)^(3)+(-2)^(2)+5`

`f(-2) = 8+4+5`

`f(-2) = 17`

x = -1

`f(-1) = -(-1)^(3)+(-1)^(2)+5`

`f(-1) = 1-1+5`

`f(-1) = 5`

x = 2

`f(2) = -(2)^(3)+(2)^(2)+5`

`f(2) = -8+4+5`

`f(2) = 1`

The range of the function is
`R=\{17, 5, 1\}`.