Question

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 - log_e2 

(B) f(2) > 1 - log_e2

(C) g(1) > 1 - log_e2 

(D) g(1) < 1 - log_e2

Answer 1

solution B,C

f'(x) = e^f(x)–g(x) .g'(x) given f(1) = g(2) = 1