Non-negative Real Roots

Let $g(x)$ be the inverse function of $f(x)=\frac{1}{24}x^2+k$ , where $x\geq 0$ . If $f(x)-g(x)$ has two distinct non-negative real roots, the range of the constant $k$ can be expressed as $a \leq k < b$ . What is the value of $a+b$ ?