# Non-negative Real Roots

Level pending

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 $$a+b$$?

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