Question

A function is shown below. What is the value of the expression f(-3) + 2f(-1) - f(4) ? *Show work* ((Explain it to me))

A. 101/36


B. 32/9


C. 4


D. 22

Answer 1

OPTION D: 22

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
`$ ((1)/(3) )^(2x) $`

We take this because -1 lies between -3 and 4.

Now, f(-1) = 2
`$ ((1)/(3) )^(2(-1)) $`

`$ \implies f(-1) = 2(3)^2 = 2(9) = $` 18

For f(4) :

Clearly, the function is:
`$ f(x) = (2x - 5)/(x - 7) $`

f(4) =
`$ (2(4) - 5)/(4 - 7) = (3)/(-3) = $` -1

Therefore, f(-3) + f(-1) - f(4) = 3 + 18 - (-1) = 3 + 18 + 1 = 22, which is OPTION D.