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  • If  and <img alt="g(x)=2x-1" src="https://entrancecorner.oncodecogs.com/gif.

If f(x)=x^2+5 and g(x)=2x-1 then which of the following is true ?

Option: 1

f(g(x)) is incresing but g(f(x)) is decreasing 


Option: 2

f(g(x)) is decresing but g(f(x)) is increasing 


Option: 3

f(g(x)) and g(f(x)) both are increasing


Option: 4

None of these


Answers (1)

\\\text{Given } \\ f(x)=x^2+5\\g(x)=2x-1 \\ f(g(x))=f(2x-1)=(2x-1)^2+5\\ f'(g(x))=4(2x-1)=8x-4 \\ g(f(x))=g(x^2+5)=2(x^2+5)-1\\ g'(f(x))=4x

As both f '(g(x)) and g '(f(x)) are linear, so they take both positive and negative values, hence they are non-monotonic functions.

Posted by

Ramraj Saini

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