Let be a differentiable function such that

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Let

f:\mathbb{R}\setminus\{-\pi,\pi\}

be a differentiable function such that

f(x) + f(y) = f\left(\frac{x+y}{1-xy}\right)

. If

f(1) = \pi

and

\lim_{x \to 0} f(x) = 2

. Then,

f(x)

is equal to (1)

2 \tan^{-1} x

(2)

\frac{1}{2} \tan^{-1} x

(3)

\frac{\pi}{2} \tan^{-1} x

(4)

2\pi \tan^{-1} x

Related theory

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