Answer:
Option D
Step-by-step explanation:
Equation of the piecewise function,
f(x) = -x² + 2x for x ≤ -3
[tex]2(\frac{1}{3})^{2x}[/tex] for -3 < x < 4
[tex]\frac{2x-5}{x-7}[/tex] for x ≥ 4
For x = -3,
f(x) = -x² + 2x
f(-3) = -(-3)² + 2(-3)
= -9 - 6
= -15
For x = -1
f(x) = [tex]2(\frac{1}{3})^{2x}[/tex]
f(-1) = [tex]2(\frac{1}{3})^{2(-1)}[/tex]
= [tex]2(\frac{1}{3})^{-2}[/tex]
= [tex]2\times 3^2[/tex]
= 18
For x = 4
f(x) = [tex]\frac{2x-5}{x-7}[/tex]
f(4) = [tex]\frac{2(4)-5}{4-7}[/tex]
= [tex]\frac{3}{-3}[/tex]
= -1
Therefore, f(-3) + 2f(-1) + f(4) = -15 + 2(18) - (-1)
= -15 + 36 + 1
= 22
Option D will be the correct option.
