Home
Class 11
MATHS
If f(x)=(ax^(2)+b)^(3), the function g s...

If `f(x)=(ax^(2)+b)^(3)`, the function g such that `f(g(x))=g(f(x))`, is given by

A

`g(x)=((b-x^(1//3))/(a))^(1//2)`

B

`g(x)=(1)/(ax^(2)+b)^(3)`

C

`g(x)=(ax^(2)+b)^(1//3)`

D

`g(x)=((x^(1//3)-b)/(a))^(1//2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

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

If f(x) and g(x) are functions such that f(x + y) = f(x) g(y) + g(x) f(y), then in |(f(alpha),g(alpha),f(alpha+theta)),(f(beta),g(beta),f(beta+theta)), (f(lambda),g(lambda),f(lambda+theta))| is independent of

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If f(x) be a function such that f(-x)= -f(x),g(x) be a function such that g(-x)= -g(x) and h(x) be a function such that h(-x)=h(x) , then choose the correct statement: I. h(f(g(-x)))=-h(f(g(x))) II. f(g(h(-x)))=f(g(h(x))) III. g(f(-x))=g(f(x))

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to (A) f(a) = g(c ) (B) f(b) = g(b) (C) f(d) = g(b) (D) f(c ) = g(a)

If f (x) is a function such that f (x) + f''(x) =0 and g (x)= (f (x))^(2) +(f' (x))^(2) and g (3) =8, then g (8)=

If f(x) is a twice differentiable function such that f'' (x) =-f(x),f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to

Let f and g be differentiable functions such that: xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R Also, f(x)gt0 and g(x)gt0 AA x in R int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R and g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R Now answer the question: f(g(0))+g(f(0))= (A) 1 (B) 2 (C) 3 (D) 4

f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The domain of the function sqrt((f(x))/(g(x))) is

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Exercise
  1. Let f (x) =x and g (x) = |x| for all . Then the function satisfying ...

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. If f(x)=(ax^(2)+b)^(3), the function g such that f(g(x))=g(f(x)), is g...

    Text Solution

    |

  4. If a function f:[2,oo)toR is defined by f(x)=x^(2)-4x+5, then the rang...

    Text Solution

    |

  5. The function f : R -> R is defined by f (x) = (x-1) (x-2) (x-3) is

    Text Solution

    |

  6. Let A={x,y,z}=B={u,v,w) and f:A to B be defined by f (x)=u, f(y)=v, f(...

    Text Solution

    |

  7. If f:R->R be defined by f(x)=x^2+1, then find f^(-1)(17) and f^(-1)(-3...

    Text Solution

    |

  8. The function f: NvecN(N is the set of natural numbers) defined by f(n)...

    Text Solution

    |

  9. The composite mapping fog of the maps f:R to R , f(x)=sin x and g:R to...

    Text Solution

    |

  10. If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

    Text Solution

    |

  11. f : R rarr R is a function defined by f (x) = 10 x - 7. If g = f^(-1),...

    Text Solution

    |

  12. Let A={x in R : xlt=1} and f: A->A be defined as f(x)=x(2-x) . Then, ...

    Text Solution

    |

  13. If f(x)=x^n , n in Nandgof(x)=ng(x) then g(x) can be

    Text Solution

    |

  14. If the function f: R->R be such that f(x)=x-[x] , where [x] denotes th...

    Text Solution

    |

  15. f:R to R given by f(x)=5-3 sin x, is

    Text Solution

    |

  16. Let f:A->B be a function defined by f(x) =sqrt3sin x +cos x+4. If f is...

    Text Solution

    |

  17. Let f: A to B; g: B to A be two functions such that gof = IA. Then; f ...

    Text Solution

    |

  18. Let f: A to B; g: B to A be two functions such that fog = IB. Then; f ...

    Text Solution

    |

  19. If f: A->B and g: B->C are one-one functions, show that gof is one-o...

    Text Solution

    |

  20. If functions f:A to B and g : B to A satisfy gof= I(A), then show that...

    Text Solution

    |