HARD
JEE Main
IMPORTANT
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Let f(x)=1-x-x3. Then, the real values of x satisfying the inequality, 1-fx-f3x>f1-5x, are

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Important Questions on Functions

MEDIUM
JEE Main
IMPORTANT
If a function satisfies x-yfx+y-x+yfx-y=2x2y-y3,  x, yR and f1=2, then
MEDIUM
JEE Main
IMPORTANT
If the fundamental period of function fx=sinx+cos(4-a2)x is 4π, then the value of a is/are:
HARD
JEE Main
IMPORTANT
Let fx be a real-valued function such that f0=12 and fx+y=fxfa-y+fyfa-x  x, yR, then for some real a:
MEDIUM
JEE Main
IMPORTANT
Which of the following functions have their range equal to R (the set of real numbers)?
HARD
JEE Main
IMPORTANT
Which of the following pairs of functions are identical?
MEDIUM
JEE Main
IMPORTANT
For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) defined as follows:
Statement I: The function fx=xsinx and f'x=xcosx+sinx are both non-periodic.
Statement II: The derivative of differentiable function (non-periodic) is non-periodic function.
MEDIUM
JEE Main
IMPORTANT
Statement I: The maximum value of sin2x+sinax cannot be 2.
(where a is positive rational number)
Statement II: 2a is irrational.