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f(x) is continous function defined in [1,5] such that f(2) =1 and f(4)=10 then the number of sollution of equation f(x) =3 in (2,.4) will be 

  • Option 1)

    1

  • Option 2)

    at least 1

  • Option 3)

    more than 1

  • Option 4)

    2

 

Answers (1)

best_answer

  As we have learned

Properties of Continuous function -

If  f  is continuous on [a, b] the f assumes at least once every value between its minimum and maximum values then there exists at least one solution of the equation f(x) = K in the open interval (a, b)

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\becausef(2)=1 and f(4)= 10 and f(x) is continous , so f(x) will take all values between 1 and 10 atleast one in the interval (2,4) , so f(x) will also be 3 , at least once in (2,4)

 

 

 

 

 


Option 1)

1

Option 2)

at least 1

Option 3)

more than 1

Option 4)

2

Posted by

Himanshu

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