Question

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

Answer 1

g(-3) =
`(17)/(4)`

g(2) = -3

g(5) =
`-(7)/(4)`

Explanation:

Let us solve the question

∵ g(x) =
`-(3)/(4)` x + 2, x ≠ 2

→ That means we can use it for any value os x except 2

∵ g(x) = -3, x = 2

→ That means we will use it only if x = 2

We want to find g(-3)

∵ x = -3 ⇒ ≠ 2

∴ We will use g(x) =
`-(3)/(4)` x + 2

→ Substitute x by -3

∵ g(-3) =
`-(3)/(4)` (-3) + 2

∴ g(-3) =
`(9)/(4)` + 2

∴ g(-3) =
`(17)/(4)`

We want to find g(2)

∵ x = 2

∴ We will use g(x) = -3

→ This is a constant function which means g(2) equal to -3

∴ g(2) = -3

We want to find g(5)

∵ x = 5 ⇒ ≠ 2

∴ We will use g(x) =
`-(3)/(4)` x + 2

→ Substitute x by 5

∵ g(5) =
`-(3)/(4)` (5) + 2

∴ g(5) =
`-(15)/(4)` + 2

∴ g(5) =
`-(7)/(4)`