True or false? The functions f(x)=12x−3 and g(x)=−2x+2 intersect at x=−2.
To determine if the functions intersect at x = -2, we can substitute -2 into both functions and check if the resulting y-values are equal.
For f(x) = 12x - 3:
f(-2) = 12(-2) - 3
= -24 - 3
= -27
For g(x) = -2x + 2:
g(-2) = -2(-2) + 2
= 4 + 2
= 6
Since -27 is not equal to 6, we conclude that the functions f(x) = 12x - 3 and g(x) = -2x + 2 do not intersect at x = -2. Therefore, the statement is false.