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I have two functions: $f(x)$ and $g(x)$.

I wonder if there is a way to mathematically express "the min of $f(x)$ and $g(x)$ intersections"?

$\min(f(x)=g(x))$ is what I could think of, but it doesn't seems right.

zj_tw
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  • David Lui's answer below is the way to go if you want the least $x$ such that $f(x) = g(x)$, and your domain is $\mathbb{R}$. If you instead want the least value of $f(x)$ such that $f(x) = g(x)$ then (for $X$ the intersection of the domains of $f$ and $g$) use $\min{({,f(x) ,\mid, f(x) = g(x),, , x \in X ,})}$. – Lemmon Oct 27 '22 at 05:39

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Use set-builder notation. You want to find the minimum of the set of intersections.

$min(\{x \in \mathbb{R} : f(x) = g(x) \})$

David Lui
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