If and is the inverse of

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

If f(x)=x+tan⁡xf(x)=x+\tan x and ff is the inverse of gg, then g′(x)g'(x) equals (1) 11+[g(x)−x]2\dfrac{1}{1+[g(x)-x]^2} (2) 12−[g(x)−x]2\dfrac{1}{2-[g(x)-x]^2} (3) 12+[g(x)−x]2\dfrac{1}{2+[g(x)-x]^2} (4) None of these

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