f(x+y) = f(x) + f(y), "for " AA x and y ...

`f(x+y) = f(x) + f(y), "for " AA x and y and f(x)= (2x^(2) + 3x) g(x)`. For `AA x`. If g(x) is a continuous function and g(0)= 3 then f'(x) = ……….

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY AND DIFFERENTIABILITY
KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice Work|96 Videos
CONTINUITY AND DIFFERENTIABILITY
KUMAR PRAKASHAN|Exercise NCERT Exemplar Problems and Solution (Short Answer Type Questions)|156 Videos
CONTINUITY AND DIFFERENTIABILITY
KUMAR PRAKASHAN|Exercise Miscellaneous Exercise - 5|46 Videos
BOARD'S QUESTION PAPER MARCH - 2020
KUMAR PRAKASHAN|Exercise PART - B (Section - C)|4 Videos
DETERMINANTS
KUMAR PRAKASHAN|Exercise Practice Paper-4 (Section-D)|2 Videos

Similar Questions

Explore conceptually related problems

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

f(x+ y) = f(x) f(y) , For AA x and y . If f(3)= 3 and f'(0) =11 then f'(3)= …….

f(x)= x + tan x and f is an inverse function of g then g'(x)= ……..

A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA x, y in R and f (x) ne 0 for any x in R . Let the function be differentiable at x = 0 and f'(0) = 2. Show that f'(x) = 2 f(x), AA x in R. Hence, determine f(x)

g(x) = 1 + sqrt(x) and f(g(x)) =3 +2sqrtx+x then f(x) = ......

If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

If f(x) - g(x) is constant then f'(x) = g'(x)

Let f(x, y) be a periodic function satisfying f(x, y) = f(2x + 2y, 2y-2x) for all x, y; Define g(x) = f(2^x,0) . Show that g(x) is a periodic function with period 12.

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook based MCQs

If x^(2) + y^(2) =t - (1)/(t) and x^(4) + y^(4) = t^(2) + (1)/(t^(2))...
Text Solution
|
If sin y= x sin (a+ y) and (dy)/(dx)= (A )/(1 + x^(2)-2x cos a) then t...
Text Solution
|
f(x+y) = f(x) + f(y), "for " AA x and y and f(x)= (2x^(2) + 3x) g(x). ...
Text Solution
|
y= sin x- cos x and f(x)= (d^(17)y)/(dx^(17)) " then " f((pi)/(4))= ……...
Text Solution
|
y= tan^(-1) ((ax-b)/(bx + a)) " then " (dy)/(dx)|(x= -1)= ………
Text Solution
|
u= f (tan x), v= g(sec x), f'(1) =2 and g'(sqrt2)= 4 " then " (du)/(d...
Text Solution
|
f(x)= sin^(2)x + sin^(2) (x + (pi)/(3)) + cos x cos (x + (pi)/(3)) the...
Text Solution
|
y= e^(3x + 7) " then " y(n) (0)=……..
Text Solution
|
x= f(t), y= phi (t) then (d^(2)y)/(dx^(2))= ……..
Text Solution
|
In the function f(x)= 2x^(3) + bx^(2) + qx satisfies conditions of Rol...
Text Solution
|
If y= (a + bx)/(c + dx), where a, b, c, d are constants and lamda y(1)...
Text Solution
|
The function f(x)= (2- root(4)(x^(2) +16))/(cos 2x-1) is continuous at...
Text Solution
|
Let f(x)= x^(3)-x^(2) + x + 1 g(x) = {max (f(t)), 0 le t le x}, 0 le x...
Text Solution
|
f(x)= |(sin x,cos x),(tan x,cot x)| then f'((pi)/(4))= …….
Text Solution
|
x= t^(2) + 3t- 8,y= 2t^(2) -2t- 4. If at point (2, -1), lamda = (dy)/(...
Text Solution
|
x=2 + t^(3), y= 2t^(2). If ((d^(2)y)/(dx^(2)))/(((dy)/(dx))^(n)) is co...
Text Solution
|
If F(x) = (1)/(x^(2)) underset(4)overset(x)int (4t^(2)- 2F'(t))dt then...
Text Solution
|
If sqrt(x^(2) + y^(2))=a. e^(tan^(-1)((y)/(x))), a gt 0 then the value...
Text Solution
|
If f(x-y), f(x).f(y) and f(x+ y) are in arithmatic progression and f(0...
Text Solution
|
[(d)/(dx) sec^(-1)x](x = -3)=…….
Text Solution
|