# Arctangent family

Calculus Level 5

In the diagram above, the black curves show some members of the family $f_c(x) = c + \arctan x.$ The red curve intersects all members of this family perpendicularly.

If the red curve is described by the function $$g$$, and $$g(0) = 0$$, how much is $$g(-6)$$?

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