Home
Class 12
MATHS
Let "g(x)" be a linear funchion and f(x)...

Let "g(x)" be a linear funchion and `f(x)={[g(x),,xle0],[((1+x)/(2+x))^((1)/(x)),,x>0]]` ,is continuous at "x=0"
If `f'(1)=f(-1)` ,then the value "g(3)" is

A

`(1)/(3)log_(e)((4)/(9e^(1/3)))`

B

`log_(e)((4)/(9))-1`

C

`log_(e)((4)/(9e^(1/3)))`

D

`(1)/(3)log_(e)((4)/(9))+1`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

Similar Questions

Explore conceptually related problems

Let g(x) be a polynomial of degree one and f(x) be defined by f(x)=-{g(x),x 0 If f(x) is continuous satisfying f'(1)=f(-1) then g(x) is

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)

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) = (1)/(1 -x) x ne 1 and g(x) = (x-1)/(x) , x ne0 , then the value of g[f(x)] is :

Let [x] denote the integral part of x in R and g(x)=x-[x]. Let f(x) be any continuous function with f(0)=f(1) then the function h(x)=f(g(x)

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2). Then the value of the integral int_(0)^(1)f(x)g(x)dx, is

Let f(x)=g(x)(e^(1//x) -e^(-1//x))/(e^(1//x) + e^(-1//x)) , where g is a continuous function then lim_(x to 0) f(x) exist if

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. Let y=y(x) be the solution of the differential equation (dy)/(dx)=((ta...

    Text Solution

    |

  2. For 0 lt c lt b lt a ,let (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 and alpha...

    Text Solution

    |

  3. Let "g(x)" be a linear funchion and f(x)={[g(x),,xle0],[((1+x)/(2+x))^...

    Text Solution

    |

  4. Let sin^(-1)alpha+sin^(-1)beta+sin^(-1)gamma=pi and alpha, beta, gamma...

    Text Solution

    |

  5. Let "S" be the set of postive integral values of "a" for which (ax^(2)...

    Text Solution

    |

  6. If f(x)=(4x-3)/(6x-4),xne2/3,g:R-{2/3}toR-{2/3},g(x)=fof(x) then value...

    Text Solution

    |

  7. Two marbles are drawn in succession from a box containing "10" red,"30...

    Text Solution

    |

  8. If f(x)=|[x^(3),2x^(2)+1,1+3x],[3x^(2)+2,2x,x^(3)+6],[x^(3)-x,4,x^(2)-...

    Text Solution

    |

  9. If the foci of a hyperbola are same as that of the ellipse (x^(2))/(9)...

    Text Solution

    |

  10. If the system of linear equations x-2y+z=-4 ; 2x+alpha y+3z=5; 3x-y+be...

    Text Solution

    |

  11. The sum of series 1/(1-3.1^2+1^4)+2/(1-3.3^2+2^4)+3/(1-3.3^2+3^4)+.......

    Text Solution

    |

  12. Let alpha,beta,gamma,delta in Z and let A(alpha,beta),B(1,0),C(gamma,d...

    Text Solution

    |

  13. A={1,2,3,4} and R={(1,2),(2,3),(1,4)} be a relation on A .Let S be the...

    Text Solution

    |

  14. In the expansion of (1-x^2)(1+x)(1+3/x+3/x^2+1/x^3)^5 the sum of the c...

    Text Solution

    |

  15. If alpha denotes the number of solutions of |1-i|^(x)=2^(x) and beta=(...

    Text Solution

    |

  16. Let vec a and vec b be two vectors such that |vec a|=1,|vec b|=4 ,and ...

    Text Solution

    |

  17. The total number of words (with or without meaning) that can be formed...

    Text Solution

    |

  18. Let S=(-1,oo) and f:S rarr R be defined as f(x)=int(-1)^(x)(e^(t)-1)^(...

    Text Solution

    |

  19. If the integral 525int(0)^((pi)/(2))sin2x cos^((11)/(2))x(1+Cos^((5)/(...

    Text Solution

    |

  20. Let the foci and length of the latus rectum of an ellipse (x^(2))/(a^(...

    Text Solution

    |