Question

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

Answer 1

Answer:

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

Step-by-step 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 $R=\{17, 5, 1\}$.