Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f...

Let `f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)),` then

`g(x)lt0,AAx in R`

`g(x)lt0, "for some " x in R`

`g(x)ge0,"for some "x in R`

`g(x)ge0,AAx in R`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|19 Videos
MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|9 Videos
MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS|Exercise Exercise For Session 5|8 Videos
MATRICES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
PAIR OF STRAIGHT LINES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^(2)-2x and g(x)=f(f(x)-1)+f(5-f(x)), then

Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x) .

Let f(x)=tan xandg(f(x))=f(x-(pi)/(4)) where f(x)andg(x) are real valued functions. Prove that f(g(x))=tan((x+1)/(x+1))

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1) =5 alpha'(2) =7 then 2nd the vlaue of beta'(1)-10

Let f(x)=1+x ln(x+sqrt((x^(2))+1))-sqrt((1)+x^(2))andh(x)=f(x)-f^(2)(x)+f^(3)(x) Then.

Let f(x)=x^(2)+xg'(1)+g''(2) and g(x)=f(1).x^(2)+xf'(x)+f''(x) then

Let f :R -{(3)/(2)}to R, f (x) = (3x+5)/(2x-3).Let f _(1) (x)=f (x), f_(n) (x)=f (f _(n-1) (x))) for pige 2, n in N, then f _(2008) (x)+ f _(2009) (x)=

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Single Option Correct Type Questions)

sinx+cosx=y^(2)-y+a has no value of x for any y, if a belongs
Text Solution
|
f:R to R is defined by f(x)==(e^(x^(2))-e^(-x^(2)))/(e^(x^(2))+e^(-x^(...
Text Solution
|
Let f(x) be a quadratic expression possible for all real x. If g(x)=...
Text Solution
|
Let f(x)=min{1,cos x,1-sinx}, -pi le x le pi, Then, f(x) is
Text Solution
|
f(x)={(2-|x^(2)+5x+6|"",xne-2),(a^(2)+1"",x=-2):},then the range of a,...
Text Solution
|
Maximum number of real solution for the equation ax^(n)+x^(2)+bx+c=0...
Text Solution
|
Maximum number area of rectangle whose two sides are x=x(0),x=pi-x(0...
Text Solution
|
f(x)=-1+kx+k neither touches nor intecepts the curve f(x)= In x, then ...
Text Solution
|
f(x) is a polynomial of degree 4 with real coefficients such that f(x)...
Text Solution
|
A curve whose concavity is directly proportional to the logarithm of i...
Text Solution
|
F(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)
Text Solution
|
If f(x) = { 3 + |x-k|, x leq k; a^2 -2 + sin(x-k)/(x-k), xgtk} has min...
Text Solution
|
Let f(x) be linear functions with the properties that f(1) le f(2), f(...
Text Solution
|
If P(x) is polynomial satisfying P(x^(2))=x^(2)P(x)andP(0)=-2, P'(3//2...
Text Solution
|
If the curve x^(2)=-4(y-a) does not intersect the curve y=[x^(2)-x...
Text Solution
|
Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then
Text Solution
|
Let f:NrarrN in such that f(n+1)gtf(f(n)) for all n in N then
Text Solution
|
The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(2) possesses
Text Solution
|
If int(0)^(x)2xf^(2)(t)dt=(int(0)^(x)2f(x-t)dt)^(2) for f(1)=1 and f(x...
Text Solution
|
A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...
Text Solution
|