Home
Class 11
MATHS
A function f: R->R satisfies the equ...

A function `f: R->R` satisfies the equation `f(x+y)=f(x)f(y)` for all`x , y in R` and `f(x)!=0 ` for all ` x in Rdot` If `f(x)` is differentiable at `x=0a n df^(prime)(0)=2,` then prove that `f^(prime)(x)=2f(x)dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

A function f: RvecR satisfies the equation f(x+y)=f(x)f(y) for all x , y in Ra n df(x)!=0fora l lx in Rdot If f(x) is differentiable at x=0a n df^(prime)(0)=2, then prove that f^(prime)(x)=2f(x)dot

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ 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

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

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

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

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

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,

A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If x=acostheta,y=bsintheta, then prove that (d^3y)/(dx^3)=(3b)/(a^3)co...

    Text Solution

    |

  2. If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a)x(dy)/(dx)-y (b) ...

    Text Solution

    |

  3. A function f: R->R satisfies the equation f(x+y)=f(x)f(y) for all...

    Text Solution

    |

  4. If u=x^2 and x=s+3t, y=2s-t, then (d^2u)/(ds^2) is (a) 5/2 t (b) 20t^...

    Text Solution

    |

  5. If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

    Text Solution

    |

  6. If f(x)=sinx+e^x , then f''(x)

    Text Solution

    |

  7. "If "y^(2)=ax^(2)+bx+c," then "y^(3)(d^(2)y)/(dx^(2)) is

    Text Solution

    |

  8. If f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(npi)/2 8| then find the val...

    Text Solution

    |

  9. Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y. If f'(0) exits...

    Text Solution

    |

  10. If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y2+x y1 is (where yr repres...

    Text Solution

    |

  11. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  12. f(x)+f(y)=f((x+y)/(1-xy)) ,for allx,yinR.(xy!=1),and lim(x->0) f(x)/x=...

    Text Solution

    |

  13. Let f: R->R satisfying |f(x)|lt=x^2,AAx in R be differentiable at x...

    Text Solution

    |

  14. If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a)11-...

    Text Solution

    |

  15. If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is

    Text Solution

    |

  16. Suppose p(x)=a0+a1x+a2x^2+...+an x^ndot If |p(x)|lt=|e^(x-1)-1| for al...

    Text Solution

    |

  17. Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)...

    Text Solution

    |

  18. A function f satisfies the condition f(x)=f^(prime)(x)+f''(x)+f'''(x)....

    Text Solution

    |

  19. Let f(x y)=f(x)f(y)AAx , y in Ra n df is differentiable at x=1 such t...

    Text Solution

    |

  20. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1...

    Text Solution

    |