Question

Use the functions f (x)= –x^2 + 8x – 11, g(x) = 14 - 2/3x,and h(x) = -x – 7 to find each function value.

1/2g(-6) + f(-2) =

Answer 1

To solve 1/2g(-6) + f(-2), we first find g(-6) which is 18, then take half of it to get 9, and calculate f(-2) which is -31. Adding both values together gives -22 as the final answer.

Step-by-step explanation:

To find the value of 1/2g(-6) + f(-2), we need to substitute the given values into the functions and perform the calculations.

First, let's evaluate g(-6). Substitute -6 into the function g(x) = 14 - (2/3)x:

g(-6) = 14 - (2/3)(-6) = 14 + 4 = 18

Next, let's evaluate f(-2). Substitute -2 into the function f(x) = -x^2 + 8x - 11:

f(-2) = -(-2)^2 + 8(-2) - 11 = -4 - 16 - 11 = -31

Now we can substitute the values into the expression and simplify:

1/2g(-6) + f(-2) = 1/2 * 18 + (-31) = 9 - 31 = -22