IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

zamuka

f : X $\rightarrow$ [1,27] is a function such that f(x) = 5sinx + 12cosx + 14 is a one-one & onto function, then X $\in$

a) [-p/2,p/2]

b) [0,p/2]

c) [0,p/2]

d) none

where p means $\pi$

ANS: none......but plz tell how to do.....

RATES ASSURED

RyuAmakusa

the min value of the fn is 1and the max value is 27 which is = to the boundaries of the range so the fn can be onto now the period of the fn. is 2pi so the fn will be onto if the gap is more then 2pi
and it will be one-one if the gap is less than 2pi so for it to be both 1-1 and onto the gap should be 2pi.which is not the there is any option if [0 2pi] was one of the option then that wud be the ans.
plz ask if some thing is not clear.

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