Question

What is the value of the expression f(-3) + 2f(-1) - f (4)

PLEASE HELP NO LINKS

Answer 1

22

Explanation:

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))`

=>
`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.