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  • Stuck here, help me understand: If gof and fog both exists then which of these is not true ?

If gof  and fog both exists then which of these is not true ?

  • Option 1)

    f(x)= g(x) 

  • Option 2)

    R_f\subseteq D_g

  • Option 3)

    R_g\subseteq D_f

  • Option 4)

    All are true 

 

Answers (1)

best_answer

As we have learned

Condition for composite function -

go f is defined only if for each x\in A, f(x) is an element of g.

- wherein

The range of f must be a subset of the domain of g.

 

 R_g\subseteq D_f  and R_f\subseteq D_g

now f(x)= g(x) is not necessarily true

 


Option 1)

f(x)= g(x) 

Option 2)

R_f\subseteq D_g

Option 3)

R_g\subseteq D_f

Option 4)

All are true 

Posted by

Himanshu

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