Let f:\mathbb{R}\to\mathbb{R} and g:\mathbb{R}\to\mathbb{R} be two non-constant differentiable functions. If f^1(x)=(e^{(f(x)-g(x))})g^1(x) for all x∊\mathbb{R},and f(1)=g(2)=1, then which of the following statement (s) is (are) TRUE? [JEE Adv 2018 P1]

Limits, Continuity and Differentiability

Section: Mathematics

Question : 25 of 51

Marks: +1, -0

Let f:ℝ→ℝ and g:ℝ→ℝ be two non-constant differentiable functions. If f1(x)=(e(f(x)−g(x)))g1(x) for all x∊ℝ,and f(1)=g(2)=1, then which of the following statement (s) is (are) TRUE?

[JEE Adv 2018 P1]

f(2)<1−loge2
f(2)>1−loge2
g(1)>1−loge2
g(1)<1−loge2

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