Answer:
OPTION D: 22
Step-by-step explanation:
Choose the function value according to the domain given.
To find f(-3) :
f(x) = x² + 2x for x ≤ -3
That means for those values of x, less than or equal to -3, this is the function.
So, f(-3) = (-3)² + 2(-3) = 9 - 6 = 3
Now, f(-1) :
From the given data, we see it is: f(x) = 2 [tex]$ (\frac{1}{3} )^{2x} $[/tex]
We take this because -1 lies between -3 and 4.
Now, f(-1) = 2 [tex]$ (\frac{1}{3} )^{2(-1)} $[/tex]
[tex]$ \implies f(-1) = 2(3)^2 = 2(9) = $[/tex] 18
For f(4) :
Clearly, the function is: [tex]$ f(x) = \frac{2x - 5}{x - 7} $[/tex]
f(4) = [tex]$ \frac{2(4) - 5}{4 - 7} = \frac{3}{-3} = $[/tex] -1
Therefore, f(-3) + f(-1) - f(4) = 3 + 18 - (-1) = 3 + 18 + 1 = 22, which is OPTION D.
