Home
Class 12
MATHS
Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in ...

Let `g(x)=f(x)-1.` If `f(x)+f(1-x)=2AAx in R ,` then `g(x)` is symmetrical about. the origin (b) `t h el in ex=1/2` the point (1,0) (d) the point `(1/2,0)`

A

the orgin

B

the line`x=(1)/(2)`

C

the point (1, 0)

D

the point `((1)/(2),0)`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)-1+f(1-x)-1=0`
So, `g(x)+g(1-x)=0.`
Replacing x by `x+(1)/(2), " we get " g((1)/(2)+x)+g((1)/(2)-x)=0.`
So, it is symmetrical about `((1)/(2), 0)`.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=f(x)-1. If f(x)+f(1-x)=2AA x in R, then g(x) is symmetrical about.(a)The origin (b) the line x=(1)/(2) the point (1,0) (d) the point ((1)/(2),0)

If f(x)+f(1-x)=2 and g(x)=f(x)-1AAx in R , then g(x) is symmetric about

Let g(x)=2f((x)/(2))+f(1-x) and f'(x)<0 in 0<=x<=1 then g(x)

Each question has four choices, a,b,c and d,out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. if both the statements are true and statement 2 is the correct explanation of statement 1. If both the statements are true but statement 2 is not the correct explanation of statement 1. If statement is True and statement2 is false. If statement1 is false and statement2 is true. Statement 1 : Ifg(x)=f(x)-1,f(x)+f(1-x)=2AAx in R ,t h e n(g(x) is symmetrical about the point 1/2,0)dot Statement 2 : If g(a-x)=-g(a+x)AAx in R , then g(x) is symmetrical about the point (a ,0)

Let f(x)=||x|-1|-1| and g(x)-(max f(t):x<=t<=x+1,x in R} The graph of g(x) is symmetrical about

Let g(x)=1+x-[x] and f(x)=-1 if x 0, then f|g(x)]=1x>0

f(x)=(x^(2))/(1+x^(3));g(t)=int f(t)dt. If g(1)=0 then g(x) equals-

Let f:Nrarr R,f(x)=2x-1 g:z rarrR,g(x)=(x^(2))/(2) , then (gof)(0) is :

Consider f(x)=int_(1)^(x)(t+(1)/(t))dt and g(x)=f'(x) If P is a point on the curve y=f(x) such that the tangent to this curve at P is parallel to the chord joining the point ((1)/(2),g((1)/(2))) and (3,g(3)) of the curve then the coordinates of the point P

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

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ...

    Text Solution

    |

  2. If f(2x+y/8,2x-y/8)=x y , then f(m , n)=0 only when m=n only when m!...

    Text Solution

    |

  3. Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(...

    Text Solution

    |

  4. If f(x+y)=f(x)+f(y)-x y-1, AA x , y in R and f(1)=1, then the number ...

    Text Solution

    |

  5. The function f satisfies the functional equation 3f(x)+2f((x+59)/(x1))...

    Text Solution

    |

  6. Let f: RrightarrowR be a continuous and differentiable function such t...

    Text Solution

    |

  7. Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...

    Text Solution

    |

  8. If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) ...

    Text Solution

    |

  9. If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...

    Text Solution

    |

  10. If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,then f(2) is equal to

    Text Solution

    |

  11. If f(3x+2)+f(3x+29)=AAx in R , then the period of f(x) is

    Text Solution

    |

  12. If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, the...

    Text Solution

    |

  13. If f(x)= maximum {x^3,x^2,1/64} AA x in[0,oo) then

    Text Solution

    |

  14. The equation ||x-2|+a|=4 can have four distinct real solutions for x i...

    Text Solution

    |

  15. Number of integral values of k for which the equation 4 cos^(-1)(-|x|)...

    Text Solution

    |

  16. If f(x) is a real-valued function defined as f(x)=In (1-sinx), then t...

    Text Solution

    |

  17. Let f(x)=x+2|x+1|+x-1|dotIf f(x)=k has exactly one real solution, then...

    Text Solution

    |

  18. The number of solutions of 2 cosx=|sinx|, 0 le x le 4 pi, is

    Text Solution

    |

  19. Let f1(x)={x, x leq x leq 1 and 1 x gt1 and 0,otherwise f2(x) =f1 (...

    Text Solution

    |

  20. If log(4)((2f(x))/(1-f(x)))=x, " then "(f(2010)+f(-2009)) is equal to

    Text Solution

    |