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  • Help me please, In which of the cases of pair of function is the composition of function is commutative ?

In which of the cases of pair of function is the composition of function is commutative ?

  • Option 1)

    f(x) = sin x   g(x) = cos x 

  • Option 2)

    f(x) =  sin x      g(x)  = x

  • Option 3)

    f(x) = sin x  g(x) = x^2

  • Option 4)

    f(x)= tan x    g (x) = cot x

 

Answers (1)

best_answer

As we have learned

Properties of composite function -

The composition of function is not commutative.

 

- wherein

f\! og \neq g\: o\! f

 

 

goI_f= I_fog=g(x)

whenever , we have an identity function gof =fog 

This is the special case for commutative property of composite function 

 

 

 

 


Option 1)

f(x) = sin x   g(x) = cos x 

Option 2)

f(x) =  sin x      g(x)  = x

Option 3)

f(x) = sin x  g(x) = x^2

Option 4)

f(x)= tan x    g (x) = cot x

Posted by

Himanshu

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