Answer:
The correct option is x = 5
Please find the attached graph of the function
Step-by-step explanation:
The given functions are;
1) f(x) = -x² + 4·x + 12
2) g(x) = x + 2
The table of values are therefore;
x, f(x), g(x)
-7, -65, -5
-6, -48, -4
-5, -33, -3
-4, -20, -2
-3, -9, -1
-2, 0, 0
-1, 7, 1
0, 12, 2
1, 15, 3
2, 16, 4
3, 15, 5
4, 12, 6
5, 7, 7
6, 0, 8
Therefore the solution to the equation f(x) = g(x), occurs at x = -2 and x = 5, where f(x) = g(x) = 0 and 7 respectively
To verify, we have;
Equating the two functions gives;
f(x) = g(x)
-x² + 4·x + 12 = x + 2
-x² + 4·x + 12 - (x + 2) = 0
-x² + 3·x + 10 = 0
(x + 2)(x - 5) = 0
x = 5 or -2
The correct option is x = 5.
