Home
Class 12
MATHS
A twice differentiable function f(x)is d...

A twice differentiable function f(x)is defined for all real numbers and satisfies the following conditions `f(0) = 2; f'(0)--5 and f '' (0) = 3`. The function `g(x)` is defined by `g(x) = e^(ax) + f (x) AA x in R`, where 'a' is any constant If `g'(0) + g''(0)=0`. Find the value(s) of 'a'

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

A function g(x) is defined g(x)=2f(x^2/2)+f(6-x^2),AA x in R such f''(x)> 0, AA x in R , then m g(x) has

A function defined for all real numbers is defined for x>-0 as follows f(x)={x|x|, 0 =1} How if f defined for x<=0 . If (i) f is even ? (ii) f is odd ?

If the functions f and g defined from the set of real number R to R such that f(x) = e^(x) and g(x) = 3x - 2, then find functions fog and gof.

A function f : R to R Satisfies the following conditions (i) f (x) ne 0 AA x in R (ii) f(x +y)= f(x) f(y) AA x, y, in R (iii) f(x) is differentiable (iv ) f'(0) =2 The derivative of f(x) satisfies the equation

Let f and g be two real values functions defined by f(x)= x + 1 and g(x) = 2x-3 . Find 1) f+g , 2) f-g , 3) f/g

If f(x)=1/x and g(x)=0 are two real functions, show that fog is not defined.

Let f and g be two real values functions defined by f ( x ) = x + 1 and g ( x ) = 2 x − 3 . Find 1) f + g , 2) f − g , 3) f / g

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)