Let f:R→Rand g:R→Rbe two non-constant differentiable functions. If fprime(x)=(e(f(x)−g(x)))gprime(x)for all x∈R, and f(1)=g(2)=1, then which of the following statement(s) is (are) TRUE?f(2) 1−(log)e2(c) g(1)>1−(log)e2(d) g(1)<1−(log)e2

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Let {f}:{R}{R}and {g}:{R}{R}be two non-constant differentiable

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Let $f : R \to R$ and $g : R \to R$ be two non-constant differentiable functions. If $f^{p r i m e} (x) = (e^{(f (x) - g (x))}) g^{p r i m e} (x)$ for all $x \in R$ , and $f (1) = g (2) = 1$ , then which of the following statement(s) is (are) TRUE? $f (2) < 1 - (lo g)_{e} 2$ (b) $f (2) > 1 - (lo g)_{e} 2$ (c) $g (1) > 1 - (lo g)_{e} 2$ (d) $g (1) < 1 - (lo g)_{e} 2$

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Elizabeth Discussed

Let

f : R \to R

and

g : R \to R

be two non-constant differentiable functions. If

f^{p r i m e} (x) = (e^{(f (x) - g (x))}) g^{p r i m e} (x)

for all

x \in R

, and

f (1) = g (2) = 1

, then which of the following statement(s) is (are) TRUE?

f (2) < 1 - (lo g)_{e} 2

(b)

f (2) > 1 - (lo g)_{e} 2

(c)

g (1) > 1 - (lo g)_{e} 2

(d)

g (1) < 1 - (lo g)_{e} 2

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Question Text	Let $f : R \to R$ and $g : R \to R$ be two non-constant differentiable functions. If $f^{p r i m e} (x) = (e^{(f (x) - g (x))}) g^{p r i m e} (x)$ for all $x \in R$ , and $f (1) = g (2) = 1$ , then which of the following statement(s) is (are) TRUE? $f (2) < 1 - (lo g)_{e} 2$ (b) $f (2) > 1 - (lo g)_{e} 2$ (c) $g (1) > 1 - (lo g)_{e} 2$ (d) $g (1) < 1 - (lo g)_{e} 2$
Answer Type	Video solution: 1
Upvotes	150