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
1
at least 1
more than 1
2
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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f(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
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