A) I, III
B) II, Ill
C) l, ll
D) All of these
Correct Answer: A
Solution :
Given, \[f:R\to R\]such that \[f(x)={{3}^{-x}}\]Let \[{{y}_{1}}\]and \[{{y}_{2}}\]be two elements of \[f(x)\]such that \[{{y}_{1}}={{y}_{2}}\] \[\Rightarrow {{3}^{-{{x}_{1}}}}={{3}^{-{{x}_{2}}}}\Rightarrow {{x}_{1}}={{x}_{2}}\] So, \[f(x)\]is one ? one. Since, \[f(x)\] is positive for every value of \[x,\]therefore \[f(x)\]is into. Now, \[f(x)={{3}^{-x}}\] \[f'(x)=-{{3}^{-x}}\log 3<0\forall x\in R\] \[\therefore \]it is decreasing function. Hence, statements I and III are true.You need to login to perform this action.
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