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If f(x)=-x^3 and g(x)=e^{-x} then which of the following is true for f(g(x)) ?

Option: 1

f(g(x)) is a increasing function


Option: 2

f(g(x)) is a strictly increasing function


Option: 3

f(g(x)) is a decreasing function


Option: 4

f(g(x)) is a strictly decreasing function


Answers (1)

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\\\text{Given }\\ f(x)=-x^3\\g(x)=e^{-x}\\ f(g(x))=-(g(x))^3=-e^{-3x}\\ f'(g(x))=3e^{-3x}>0\Rightarrow strictly\ increasing \\

We can also see from the graphs of f(x) and g(x) that both of these are strictly decreasing functions. Hence their composition f(g(x)) is a strictly increasing function

 

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Ritika Jonwal

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