Question

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

please help! WILL GIVE 40 points!

Answer 1

For this question, you must substitute g(x) into -1/2x-2 if x≠2 and substitute g(x) into 2 if x=2. This explains the following:

g(-5)= -1/2(-5)-2= -1/2, since x≠2
g(2)= 2, since x=2
g(5)= -1/2(5)-2= -9/2, since x≠2

Answer 2

g(- 5) =
`(1)/(2)` , g(2) = 2 , g(5) = -
`(9)/(2)`

Explanation:

g(- 5) with x = - 5 ,in interval x ≠ 2, then g(x) = -
`(1)/(2)` x - 2 , so

g(- 5) = -
`(1)/(2)` (- 5) - 2 =
`(5)/(2)` - 2 =
`(5)/(2)` -
`(4)/(2)` =
`(1)/(2)`

g(2) with x = 2 then g(x) = 2 , so

g(2) = 2

g(5) with x = 5, in interval x ≠ 2, then g(x) = -
`(1)/(2)` x - 2 , so

g(5) = -
`(1)/(2)` (5) - 2 = -
`(5)/(2)` - 2 = -
`(5)/(2)` -
`(4)/(2)` = -
`(9)/(2)`