MEDIUM
JEE Main
IMPORTANT
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If the function f:[1,)[1,) is defined by fx=2xx-1, then f-1x is

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Important Questions on Functions

MEDIUM
JEE Main
IMPORTANT
Let f:-π3,2π3[0,4] be a function defined as fx=3sinx-cosx+2. Then f-1x is given by
HARD
JEE Main
IMPORTANT
If fx=-x+1,x0-x-12,x1 then the number of solution(s) of fx-f-1x=0 is
HARD
JEE Main
IMPORTANT
If fx=x2+x+34 and gx=x2+ax+1 be two real functions, then the range of a for which gfx=0 has no real solution, is
MEDIUM
JEE Main
IMPORTANT
A function f from integers to integers is defined as fx=n+3,noddn2,neven suppose k odd and fffk=27, then the sum of digits of k, is:
HARD
JEE Main
IMPORTANT
For any real number x, let [x] denote the integer part of x; {x} be the fractional part of x. x=x-x. Let A denote the set of all real numbers x satisfying x=x+x+x+1220. If S is the sum of all numbers in A, find S.
MEDIUM
JEE Main
IMPORTANT
The period of the function csin2x+sin2x+π3+cosxcosx+π3 is (where c is constant)
HARD
JEE Main
IMPORTANT
Let f and g be functions defined by fx=1x+1, xR, x-1 and g(x)=x2+1,xR. Then, gof is
MEDIUM
JEE Main
IMPORTANT
If fx and gx are periodic functions with periods 7 and 11, respectively. Then, the period of Fx=fx·gx5+gx·fx3 is