Okay, here we have this:
Considering the provided functions, we are going to complete the requested table, so we obtain the following:
f(1):
f(x) = −x² + 4x + 12
f(1) = −1² + 4(1) + 12
f(1) = −1 + 4 + 12
f(1) = 15
f(2):
f(x) = −x² + 4x + 12
f(2) = −2² + 4(2) + 12
f(2) = −4 + 8 + 12
f(2) = 16
f(3):
f(x) = −x² + 4x + 12
f(3) = −3² + 4(3) + 12
f(3) = −9 + 12 + 12
f(3) = 15
f(4):
f(x) = −x² + 4x + 12
f(4) = −4² + 4(4) + 12
f(4) = −16 + 16 + 12
f(4) = 12
f(5):
f(x) = −x² + 4x + 12
f(5) = −5² + 4(5) + 12
f(5) = −25 + 20 + 12
f(5) = 7
f(6):
f(x) = −x² + 4x + 12
f(6) = −6² + 4(6) + 12
f(6) = −36 + 24 + 12
f(6) = 0
g(1):
g(x)=x+2
g(1)=1+2
g(1)=3
g(2):
g(x)=x+2
g(2)=2+2
g(2)=4
g(3):
g(x)=x+2
g(3)=3+2
g(3)=5
g(4):
g(x)=x+2
g(4)=4+2
g(4)=6
g(5):
g(x)=x+2
g(5)=5+2
g(5)=7
g(6):
g(x)=x+2
g(6)=6+2
g(6)=8
And now we will proceed to find the solution of f(x)=g(x):
f(x)=g(x)
−x² + 4x + 12=x+2
−x² + 3x + 10=0
-(x+2)(x-5)=0
Then:
x+2=0 or x-5=0
x=-2 or x=5
Finally we obtain that the values that are solution to f(x)=g(x) are -2 and 5. Then the correct answer is the third option.