Answer:
The range of the function is [tex]R=\{17, 5, 1\}[/tex].
Step-by-step explanation:
Let [tex]f(x) = -x^{3}+x^{2}+5[/tex]. 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
[tex]f(-2) = -(-2)^{3}+(-2)^{2}+5[/tex]
[tex]f(-2) = 8+4+5[/tex]
[tex]f(-2) = 17[/tex]
x = -1
[tex]f(-1) = -(-1)^{3}+(-1)^{2}+5[/tex]
[tex]f(-1) = 1-1+5[/tex]
[tex]f(-1) = 5[/tex]
x = 2
[tex]f(2) = -(2)^{3}+(2)^{2}+5[/tex]
[tex]f(2) = -8+4+5[/tex]
[tex]f(2) = 1[/tex]
The range of the function is [tex]R=\{17, 5, 1\}[/tex].
