Question

Suppose that the function f is defined, for all real numbers, as follows.

Find f(-5), f(-2), and f(2).

Answer 1

-
`(10)/(3)` , 2 ,
`(11)/(3)`

Explanation:

f(- 5) with x = - 5 ≠ - 2, then f(x) = -
`(1)/(3)` x² + 5 , that is

f(- 5) = -
`(1)/(3)` (- 5)² + 5

= -
`(1)/(3)` (25) + 5

= -
`(25)/(3)` +
`(15)/(3)`

= -
`(10)/(3)`

----------------------------

f(- 2) with x = - 2 , then f(x) = 2 , that is

f(- 2) = 2

----------------------------

f(2) with x = 2 ≠ - 2 , then f(x) = -
`(1)/(3)` x² + 5 , that is

f(2) = -
`(1)/(3)` (2)² + 5

= -
`(1)/(3)` (4) + 5

= -
`(4)/(3)` +
`(15)/(3)`

=
`(11)/(3)`