f(x)≤x²/2+8x+28 is a function and it can be plotted by first changing the less-than-or-equal-to sign to an equals sign. This gives us the graph of a parabola (U-shaped curve). The less-than-or-equal-to sign represents the area below the curve, which is an infinite area because it includes everything below the x-axis as well as the area between the curve and above the x-axis. It also includes all points on the curve itself.
So the function has been defined in this way and no further “solution” is possible or is required.
