Two functions are shown in the table below: Function
1
2 3 4 5 6
f(x) = -x2 + 4x + 12
g(x) = x + 2
Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).
O x = 2
Ox= 3
O x = 5
O x = 6

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.

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