Home
Class 12
MATHS
Let f:""(-1,""1) rarr R be a differentia...

Let `f:""(-1,""1) rarr R` be a differentiable function with `f(0)""=""-1" "a n d" "f'(0)""=""1` . Let `g(x)""=""[f(2f(x)""+""2)]^2` . Then `g'(0)""=` (1) `-4` (2) 0 (3) `2` (4) 4

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let f:""(1,""1)vecR be a differentiable functio with f(0)""=""-1""a n d""f'(0)""=""1 . Let g(x)""=""[f(2f(x)""+""2)]^2 . Then g'(0)""= (1) 4 (2) 0 (3) 2 (4) -4

Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) = If g(x)=(f(2f^(2)(x)+2))^(2), then g'(0) equals

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

Let f : R rarr R : f(x) = (2x-3)/(4) be an invertible function. Find f^(-1) .

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x)

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2 and f(1)=1, then

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , 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

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

    Text Solution

    |

  2. If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...

    Text Solution

    |

  3. Let f:""(-1,""1) rarr R be a differentiable function with f(0)""=""-...

    Text Solution

    |

  4. Let y be an implicit function of x defined by x^(2x)-2x^(x) cot y-1=0...

    Text Solution

    |

  5. If x^m y^n=(x+y)^(m+n), prove that (dy)/(dx)=y/x .

    Text Solution

    |

  6. The function f(x)=sqrt(a x^3+b x^2+c x+d) has its non-zero local mini...

    Text Solution

    |

  7. If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h...

    Text Solution

    |

  8. STATEMENT 1 : When a polynomial P(x)(d egr e e >2) is divided by (x-1)...

    Text Solution

    |

  9. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

    Text Solution

    |

  10. Solve each of the following system of equations in Rdot |x-1|+|x-2...

    Text Solution

    |

  11. The complete solution set of the inequation sqrt(x+18)<2-x , is (-18 ,...

    Text Solution

    |

  12. If (lim)(xvecoo)(2+(f(x))/(x^2))^(1/x)=e and f(x)=a0+a1x+a2x^3+ , then

    Text Solution

    |

  13. The matrix A has x rows and (x+5) column. If the matrix B has y rows a...

    Text Solution

    |

  14. If y=xln((a x)^(-1)+a^(-1)) prove that x(x+1)(d^2y)/(dx^2)+(dy)/(dx)=y...

    Text Solution

    |

  15. If the solution of the equation |(x^4-9)-(x^2+3)|=|x^4-9|-|x^2+3| is ...

    Text Solution

    |

  16. In the given figure (circle), P T=5,P D=7a n dP A=2, then the value of...

    Text Solution

    |

  17. Consider the matrices A=[(4,6,-1),(3,0,2),(1,-2,5)], B=[(2,4),(0,1),(...

    Text Solution

    |

  18. The solution set of the equation (x+1)log(3)^(2)x+4xlog(3)-16=0is

    Text Solution

    |

  19. If y = f(x),has following graph Match the column by filling follo...

    Text Solution

    |

  20. Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not eq...

    Text Solution

    |