If f (x) is a function such that f (x) +...

If `f (x)` is a function such that `f (x) + f'(x) =0 and g (x)= (f (x))^(2) +(f' (x))^(2) and g (3) =8,` rhen `g (8)=`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|36 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|32 Videos
COMPOUND ANGLES
VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|31 Videos
DETERMINANTS
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

If f(x) is polynomial function such that f(x)+f'(x)+f(x)+f'(x)=x^(3) and g(x)=int(f(x))/(x^(3)) and g(1)=1 then g( e ) is

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

Let f(x) be a function such that f(x)*f(y)=f(x+y),f(0)=1,f(1)=4. If 2g(x)=f(x)*(1-g(x))

If f(x)=(ax^(2)+b)^(3), then find the function g such that f(g(x))=g(f(x))

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0

If f(x)=|x-1| and g(x)=f(f(f(x))) then for x>2,g'(x)=

g(x) is inverse function of f(x). find f'(x) or f'(1) if g(x)=x^(^^)3+e^(^^)(x/2)

VIKAS GUPTA (BLACK BOOK)-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)

If f (x) is a function such that f (x) + f'(x) =0 and g (x)= (f (x))^(...
Text Solution
|
Let f (x)= {{:(ac (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 ^(3)), where k ...
Text Solution
|
The number of values of x , x I [-2,3] where f (x) =[x ^(2)] sin (pix)...
Text Solution
|
If f (x) is continous and fifferentiable in [-3,9] and f'(x) in [-2,8]...
Text Solution
|
In f (x)= [{:(cos x ^(3),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...
Text Solution
|
Let f (x) =x ^(2) +ax+3 and g (x) =x+b, where F (x) =lim (xto oo) (f(x...
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) +2AA 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 (piy)+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=e^(2 sin ^(-1)x) then |((x ^(2) -1) y ^('') +xy')/(y)| is equal t...
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
|
Let f :R to R be a differentiable function satisfying: f (xy) =(f(x)...
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
|