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  • Help me please, Which of the following statement is true , when it is given that f(x) is a continous function from [a,b] onto [a,b] then

Which of the following statement is true , when it is given that f(x) is a continous function from [a,b] onto [a,b] then

  • Option 1)

    for some x\epsilon [a,b] ; f(x)=x

  • Option 2)

    for some x\epsilon [a,b] ; f(x)=x^{2}

  • Option 3)

    for some x\epsilon [a,b] ; f(x)=x^{3}

  • Option 4)

    for some x\epsilon [a,b] ; f(x)=x^{4}

 

Answers (1)

best_answer

As we have learned

Properties of Continuous function -

If  f  is continuous on [a, b]  and  maps [a, b] into [a, b]  then for some   x\epsilon [a, b]   we have f(x) = x.

-

 

When f(x) is continous in [a,b] and maps [a,b] into [a,b] then there are some n \epsilon [a,b] for which f(x =x

 

 

 

 

 

 


Option 1)

for some x\epsilon [a,b] ; f(x)=x

Option 2)

for some x\epsilon [a,b] ; f(x)=x^{2}

Option 3)

for some x\epsilon [a,b] ; f(x)=x^{3}

Option 4)

for some x\epsilon [a,b] ; f(x)=x^{4}

Posted by

Himanshu

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