Answer:
-3
Explanation:
You want the smallest k such that g(x) = 7-2x²-12x has an inverse function for x>k.
Inverse function
The inverse of g(x) will exist if it passes the horizontal line test. That is, a horizontal line can intersect g(x) in no more than one place.
This will be the case when x-values are restricted to those greater than the x-value of the line of symmetry.
Line of symmetry
The line of symmetry of function g(x) = ax² +bx +c is given by ...
x = -b/(2a)
The given function has a=-2, b=-12, and c=7. The line of symmetry is ...
x = -(-12)/(2(-2)) = 12/-4 = -3
g(x) will have an inverse for all x > -3.