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  • If  and <img alt="g(x)=x^4-8" src="https://learn.careers360.com/latex-image/?g%28x%29%3Dx

If f(x)=|x-8| and g(x)=x^4-8 then f(g(x)) is ?

Option: 1

monotonicly increasing function 


Option: 2

monotonicly decreasing function 


Option: 3

non-monotonicly function 


Option: 4

None of these


Answers (1)

best_answer

 

 

Non-Monotonic Function and Critical Point -

Non-Monotonic Function and Critical Point

A function which are neither always increasing nor always decreasing. Such functions are called Non-monotonic functions.

Critical Point:

The critical point of a function is when its derivative does not exist or its derivative is equal to zero.

All the values of ‘x’ obtained by bellow conditions are said to be the critical points.

  1. f(x) does not exists

  2. f’(x) does not exists

  3. f’(x) = 0.

Critical points are interior points of the intervals.

-

 

 

\text{Given }\\ f(x)=|x-8|\\ g(x)=x^4-8\\ f(g(x))=|x^4-16|

clearly f(g(x)) is not differentiable at 2 and -2

Posted by

Rishi

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