Let f: R R and g: R R be two non-constant differentiable functions. If f'(x) =...
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Let f: R R and g: R R be two non-constant differentiable functions. If f'(x) = (e(f(x)-g(x)) g'(x) for all x R, and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE? (A) f(2) <1-loge 2 (C) g(1) > 1-loge 2 (B) f(2)> 1-loge 2 (D) g(1) <1-loge 2 Let f: R R and g: R R be two non-constant differentiable functions. If f'(x) = (e(f(x)-g(x)) g'(x) for all x R, and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE? (A) f(2) <1-loge 2 (C) g(1) > 1-loge 2 (B) f(2)> 1-loge 2 (D) g(1) <1-loge 2
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