Let f :R to R is not identically zero, d...

Let `f :R to R` is not identically zero, differentiable function and satisfy the equals `d (xy)= f(x) f(y) and f (x+z) + f(x) + f (a),` then `f (5)=`

A

3

B

5

C

10

D

15

Text Solution

Verified by Experts

The correct Answer is:

B

Topper's Solved these Questions

CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|35 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|29 Videos
COMPOUND ANGLES
VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
DETERMINANTS
VK JAISWAL ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

Let f :R to R is not identically zero, differentiable function and satisfy the equals f(xy)= f(x) f(y) and f (x+z) = f(x) + f (z), then f (5)=

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

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

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

Let f :R ^(+) to R be a differentiable function with f (1)=3 and satisfying : int _(1) ^(xy) f(t) dt =y int_(1) ^(x) f (t) dt +x int_(1) ^(y) f (t) dt AA x, y in R^(+), then f (e) =

Let f be a differential function satisfying the condition. f((x)/(y))=(f(x))/(f(y))"for all "x,y ( ne 0) in R"and f(y) ne 0 If f'(1)=2 , then f'(x) is equal to

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

VK JAISWAL ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Let f :R to R is not identically zero, differentiable function and sat...
Text Solution
|
Let f (x)= {{:(ax (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...
Text Solution
|
If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...
Text Solution
|
If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...
Text Solution
|
The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix)...
Text Solution
|
If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...
Text Solution
|
In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...
Text Solution
|
Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim( n to oo) (f...
Text Solution
|
Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...
Text Solution
|
If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable...
Text Solution
|
Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...
Text Solution
|
If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...
Text Solution
|
f (x) =a cos (pix)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...
Text Solution
|
Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...
Text Solution
|
Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...
Text Solution
|
If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y^('') +xy')/(y)| is equal to
Text Solution
|
Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...
Text Solution
|
In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...
Text Solution
|
For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...
Text Solution
|
Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...
Text Solution
|
If x = cos theta and y = sin^(3) theta, then |(yd ^(2)y)/(dx ^(2))+((d...
Text Solution
|