Home
Class 12
MATHS
If f: RvecQ (rational numbers), g: RvecQ...

If `f: RvecQ` (rational numbers), `g: RvecQ` (Rational number ) are two continuous functions such that `sqrt(3)f(x)+g(x)=4,` then `(1-f(x))^3+(g(x)-3)^3` is equal to a. 1 b. 2 c. 3 d. 4

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`f:RrarrQand g:RrarrQ, "but"sqrt3f(x)+g(x)=4` it is trure only.
when `f(x)=0rArrg(x)=4`
`therefore" "(1-f(x))^(3)+(g(x)-3)^(3)=2`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE|Exercise Multiple Correct Answers Type|10 Videos

  • FUNCTIONS

    CENGAGE|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE|Exercise DPP 3.4|18 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE|Exercise Exercise|18 Videos

Similar Questions

Explore conceptually related problems

If f: R->Q (rational numbers), g: R->Q (Rational number ) are two continuous functions such that sqrt(3)f(x)+g(x)=4, then (1-f(x))^3+(g(x)-3)^3 is equal to a. 1 b. 2 c. 3 d. 4

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

If f and g are continuous functions with f(3)=5 and lim_(x to 3)[2f(x)-g(x)]=4 , find g(3).

If f and g are continuous functions with f(3) = 5 and lim_(xto3)[2f(x)-g(x)]=4 , find g(3).

Let f(x)a n dg(x) be two continuous functions defined from RvecR , such that f(x_1)>f(x_2)a n dg(x_1) f(g(3alpha-4))

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

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

Let f be a continuous function on [2, 5]. If f takes only rational values for all x and f(3) = 12, then f(4.5) is equal to

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

CENGAGE-FUNCTIONS-Question Bank
  1. If f: RvecQ (rational numbers), g: RvecQ (Rational number ) are two co...

    Text Solution

    |

  2. If there are four distinct real numbers satisfying thẻ equation |x^2-4...

    Text Solution

    |

  3. Let f: R rarr R be a polynomial function satisfying f(f(x) -2 y)=2 x-3...

    Text Solution

    |

  4. Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1, P(2)=...

    Text Solution

    |

  5. A function f(x) is such that f(x)=0 has 8 distinct real roots and f(4+...

    Text Solution

    |

  6. The number of integral values of x satisfying the equation sgn([15/(1+...

    Text Solution

    |

  7. Let f(x)=(1-c x)/(1-c^2) . If f(x) gt 0 for évery x greater than zero....

    Text Solution

    |

  8. Let g:[-2,2] rarr R, where g(x)=x^(2015)+sgn(x)+[(x^2+1)/p] be an odd ...

    Text Solution

    |

  9. If f(x)=|x+2|+|2 x-p|+|x-2| attains its minimum value in the interval ...

    Text Solution

    |

  10. Let the function f: R rarr R be defined as f(x)=min .(x+2,4-2 x, 1+4 x...

    Text Solution

    |

  11. Let f: R rarr R be defined as f(x)=2 x^3+7 x-5 and g(x)=f^-1(x). If g^...

    Text Solution

    |

  12. If f(x)= 3 sqrt((9)/(log2 (3-2x) - 1) then the value of ' a ' which sa...

    Text Solution

    |

  13. Consider the function f(x)=sqrt(2-x)+sqrt(1+x). If d denotes the numb...

    Text Solution

    |

  14. If f(x, y)=(max (x, y))^(min (x, y)) and g(x, y)=max (x, y) -min (x, y...

    Text Solution

    |

  15. The number of solution of the equation e^(2 x) + e^x+e^-(2 x)+ e^(-x...

    Text Solution

    |

  16. Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integ...

    Text Solution

    |

  17. Let f:R->R be a continuous function such that|f(x)-f(y)|>=|x-y| for a...

    Text Solution

    |

  18. Let the equation (a-1) x^2=x(2 b+3) be satisfied by three distinct val...

    Text Solution

    |

  19. f(x) = (2x^(2) + 3)/(5), for oo lt x le 1 = 6 -5x, for 1 lt x lt 3 ...

    Text Solution

    |

  20. Let f(x)=x/(1-x) and ' a ' be a real number. If x0=a, x1=f(x0) , x2=f(...

    Text Solution

    |

  21. If the largest positive value of the function defined as f(x)=sqrt(8 x...

    Text Solution

    |