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Question

The function f:RR is defined by f(x)=cos2 x+sin64 x. Then, f(R) =


  1. [34,1)

  2. (34,1]

  3. [34,1]

  4. (34,1)


Solution

The correct option is C

[34,1]


Given:
f(x)=cos2 x+sin4 xf(x)=1sin2 x+sin4 xf(x)=(sin2 x12)2+34
The minimum value of f(x) is 34
Also,
sin2 x1sin2 x1212(sin2 x12)214(sin2 x12)2+3414+34f(x)1
The maximum value of f(x) is 1.

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