Let f be a differentiable function satis...

Let f be a differentiable function satisfying `f'(x)=f' (-x) AA x in R.` Then

If `f (1) =f (2), ` then `f (-1)=f (-2)`

`1/2 f (x)+ 1/2 f (y) =f ((1)/(2) (x+y)))` for all ral values of x,y

Let `f (x)` be an even function, then `f (x) =0 AA x in R`

`f(x) +f (-x) =2f (o) AA x in R`

Text Solution

Verified by Experts

The correct Answer is:

A, D

Topper's Solved these Questions

CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|32 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|1 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|23 Videos
COMPOUND ANGLES
VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|31 Videos
DETERMINANTS
VK JAISWAL|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|11 Videos

Similar Questions

Explore conceptually related problems

Let f be a differentiable function satisfying f '(x) =2 f(x) +10 AA x in R and f (0) =0, then the number of real roots of the equation f (x)+ 5 sec ^(2) x=0 ln (0, 2pi) is:

Let f : R rarr R be a differentiable function satisfying f(x) = f(y) f(x - y), AA x, y in R and f'(0) = int_(0)^(4) {2x}dx , where {.} denotes the fractional part function and f'(-3) - alpha e^(beta) . Then, |alpha + beta| is equal to.......

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx)

Let f be a differentiable function satisfying f(x+2y)=2yf(x)+xf(y)-3xy+1 AA x , y in R such that f'(0)=1 ,then value of f(8) is equal

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

If f(x) is a differentiable function satisfying |f'(x)| le 2 AA x in [0, 4] and f(0)=0 , then

If f is a differentiable function satisfying 2f(x)=f(xy)+f((x)/(y)),AA x,y in R^(+), f(1)=0 and f'(1)=(1)/(ln6), then f(7776) =

VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)

If f(x) = |sinx|, then
Text Solution
|
Let [.] represent the greatest integer function and f (x)=[tan^2 x] th...
Text Solution
|
Let f be a differentiable function satisfying f'(x)=f' (-x) AA x in R....
Text Solution
|
Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n i...
Text Solution
|
Let f (x) =[x] and g (x) =0 when x is an integer and g (x) =x ^(2) whe...
Text Solution
|
Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...
Text Solution
|
Let f (x) =|2x-9|+|2x+9|. Which of the following are true ?
Text Solution
|
Let f (x)= max (x,x ^(2) x ^(3)) in -2 le x le 2. Then:
Text Solution
|
Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA, x...
Text Solution
|
Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...
Text Solution
|
let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...
Text Solution
|
If y =e ^(x sin (x ^(3)))+(tan x)^(x) then (dy)/(dx) may be equal to:
Text Solution
|
Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x...
Text Solution
|
Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...
Text Solution
|
If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),...
Text Solution
|
If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) ...
Text Solution
|
Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f ('(x)...
Text Solution
|
If f(x)={|x|-3 x < 1|x-2|+a x >= 1 & g(x)={2-|x| x < 2 sgn(x)-b x >= 2...
Text Solution
|
Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln...
Text Solution
|
f (x) is differentiable function satisfying the relationship f ^(2) (x...
Text Solution
|