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  • if  and <img alt="g(x)=5x-3" src="https://entrancecorner.oncodecogs.com/gif.latex?g%28x%2

if f(x)=x^3 and g(x)=5x-3 then which of the following is true ? 

Option: 1

f(g(x)) is increasing function but g(f(x)) is decreasing function 


Option: 2

f(g(x)) is  decreasing function but g(f(x)) is increasing function 


Option: 3

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


Option: 4

f(g(x)) and  g(f(x)) both are decreasing function 


Answers (1)

best_answer

\\\text{Given }\\ f(x)=x^3 \ and \ g(x)=5x-3 \\ f(g(x))=f(5x-3)=(5x-3)^3\\ f'(g(x))=3\times 5(5x-3)^2 \geq 0\\ g(f(x))=g(x^3)=5x^3-5\\ g'(f(x))=15x^2 \geq 0\\

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

 

Method 2

Also as both f(x) and g(x) are increasing functions, so their composite functions f(g(x)) and g(f(x)) are increasing functions as well.

Posted by

Ritika Harsh

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