Question

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

Answer 1

(a) We use the given g(x) to find the values

g(-1), Here x = -1 which is x<=-2

so we use g(x) =
`(1)/(4) x - 1`

Plug in -1 for x

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

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

(b) g(1), Here x=1 and it comes under the interval x>=1

so we use g(x) = -2

g(1) = -2

(c) g(4), Here x=4 and it comes under the interval x>=1 because 4 is greater than 1. so we use g(x) = -2

g(4) = -2