Shortest Chord from origin to function

Question

worked solution:

Is this found using the distance of a line equation, where instead of co-ordinate points they use functions, so the two functions are g(x) and x (because the origin is on the line y=x)

Answer 1

A point $Q$ on the graph has coordinates $Q=(x_Q,g(x_Q))$. The origin $O$ has coordinates $O=(0,0)$. The distance between two points $P_1=(x_1,y_1)$ and $P_2=(x_2,y_2)$ is $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$. In your case you will get that $d$ is a function of $x_Q$. The minimum of this function gives what you are searching for.