Let f: R->R be given by f(x)=[x]^2+[x+1]...

Let `f: R->R` be given by `f(x)=[x]^2+[x+1]-3` , where `[x]` denotes the greatest integer less than or equal to `x` . Then, `f(x)` is (a) many-one and onto (b) many-one and into (c) one-one and into (d) one-one and onto

Topper's Solved these Questions

INVERSE TRIGONOMETRIC FUNCTIONS
RESONANCE DPP|Exercise All Questions|15 Videos
MATRICES
RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

let f:R rarr R be given by f(x)=[x]^(2)+[x+1]-3, where [x] denotes the greatest integer less than or equal to x. Then,f(x) is

f: N rarr N, where f(x)=x-(-1)^(x) .Then f is: (a)one-one and into (b)many-one and into (c)one-one and onto (d)many-one and onto

The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and onto (b) many-one and onto (c) one-one and into (d) many-one and into

The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and onto (b) many one and onto (c) one-one and into (d) many one and into

Let f:R rarr R, be defined as f(x)=e^(x^(2))+cos x, then is (a) one-one and onto (b) one-one and into ( c) many-one and onto (d) many-one and into

The function f:(-oo,-1)rarr(0,e^(5)) defined by f(x)=e^(x^(3)-3x+2) is (a)many one and onto (b)many one and into (c)one-one and onto (d)one-one and into

Let f:R^(+)rarr{-1,0,1} defined by f(x)=sgn(x-x^(4)+x^(7)-x^(8)-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into one-one and onto (4) one- one and into

the function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). f(x) is (A) one-one and onto (B) one-one and into (C) many-one and onto (D) many-one and into

f: R rarr R,f(x)=x|x| is (A) one-one but not onto (B) onto but not one-one (C) Both one-one and onto (D) neither one-one nor onto

RESONANCE DPP-JEE MAINS-All Questions

Which pair(s) of function(s) is/are equal? f(x) = cos(2tan^-1 x) ;g(x)...
Text Solution
|
Which of the following are true for the inequation (x-1)(x-2)(x-4)(x-9...
Text Solution
|
Let f: R->R be given by f(x)=[x]^2+[x+1]-3 , where [x] denotes the gre...
Text Solution
|
Complete solution set of the inequation (x^2-1)(x^2-6x+8)geq0 is (a...
Text Solution
|
If domain of f(x) be (-1, 2), then (1) domain of f(sin x) will be (-oo...
Text Solution
|
If a+b+c=0 and a^2+b^2+c^2=1, then (a) a b+b c+c a=1/2 (b) a b+b...
Text Solution
|
If f(x)=2 tan 3x+5sqrt(1-cos 6x) ; g(x) is a function having the same...
Text Solution
|
The greatest ' x ' satisfying the inequation (2x+1)/3-(3x-1)/2>1 is: -...
Text Solution
|
If (x-1)(x-3)(x+2)(x-5)>0 then ' x^(prime) can be [6,8] (b) [2, 3] (c...
Text Solution
|
In the figure, if A B=A C ,/B A D=30^0 and A E=A D , then x is equal t...
Text Solution
|
Number of composite numbers less than 20 which are coprime with 4 s...
Text Solution
|
Number of integrs less than 15 satisfying the equation 2^(|x+1|)-2^x=...
Text Solution
|
If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx)a tx=0i s -3/(10) ...
Text Solution
|
The least value of x satisfying the equation 2^(|x+1|)-2^x=|2^x-1|+1...
Text Solution
|
If f(x)=4x^3-x^2-2x+1 and g(x)=min{f(t): 0lt=tlt=x} : 0lt=xlt=1 and g(...
Text Solution
|
Let aa n db be the number of solutions and sum of solutions of (2x)/(x...
Text Solution
|
If xcosy+ycosx=pi then the value of y^(0) is equal to pi (b) -pi (c)...
Text Solution
|
The simultaneous equations, y=x+2|x|& y=4+x-|x| have the solution...
Text Solution
|
If f^(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 an...
Text Solution
|
The minimum value of the expression |x-p+|x-15|+|x-p-15| for ' x ' in ...
Text Solution
|