Question

What is the value of the expression? Show your work

Answer 1

Option D

Explanation:

Equation of the piecewise function,

f(x) = -x² + 2x for x ≤ -3

`2((1)/(3))^(2x)` for -3 < x < 4

`(2x-5)/(x-7)` for x ≥ 4

For x = -3,

f(x) = -x² + 2x

f(-3) = -(-3)² + 2(-3)

= -9 - 6

= -15

For x = -1

f(x) =
`2((1)/(3))^(2x)`

f(-1) =
`2((1)/(3))^(2(-1))`

=
`2((1)/(3))^(-2)`

=
`2* 3^2`

= 18

For x = 4

f(x) =
`(2x-5)/(x-7)`

f(4) =
`(2(4)-5)/(4-7)`

=
`(3)/(-3)`

= -1

Therefore, f(-3) + 2f(-1) + f(4) = -15 + 2(18) - (-1)

= -15 + 36 + 1

= 22

Option D will be the correct option.