Home
Class 12
MATHS
Identify the type of the functions: f(x)...

Identify the type of the functions: `f(x)={g(x)-g(-x)}^(3)`

A

Odd

B

Even

C

Neither

D

Both

Text Solution

Verified by Experts

The correct Answer is:
A
`f(-x)=(g(-x)-g(x))^(3)= -(g(x)-g(-x))^(3)= -f(x)`
Hence, `f(x)` is an odd function.
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Identify the following functions : f(x)=xg(x)g(-x)+"tan"(sinx)

If e^(A) is defined as e^(A)=I+A+A^(2)/(2!)+A^(3)/(3!)+...=1/2 [(f(x),g(x)),(g(x),f(x))] , where A=[(x,x),(x,x)], 0 lt x lt 1 and I is identity matrix, then find the functions f(x) and g(x).

If g is the inverse of a function f and f'(x)=(1)/(1+x^(5)) , then g'(x) is equal to-

If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of f(x)=f(x)g(x/5)-g(x)f(x/3) is

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

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

Let f and g be two functions defined by f(x)=(x)/(x+1), g(x) =(x)/(1-x) . If ( f o g ) ^(-1) (x) is equal to kx, then find the value of k.

If the inverse function of y=f(x) is x=g(y) and f'(x)=(1)/(1+x^(2)) , then prove that g'(x)=1+[g(x)]^(2) .

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^(2) .Prove that, int_(0)^(1)f(x)g(x)dx=(1)/(2)(2e-e^(2)-3)

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Consider the function: f(x)=m a xdot{1,|x-1|, min {4,|3x-1|}}AAx in ...

    Text Solution

    |

  2. Find the equivalent definition of f(x)=m a xdot{x^2,(-x)^2,2x(1-x)}w h...

    Text Solution

    |

  3. Identify the type of the functions: f(x)={g(x)-g(-x)}^(3)

    Text Solution

    |

  4. Identify the following functions whether odd or even or neither: f(x)=...

    Text Solution

    |

  5. Identify the following functions : f(x)=xg(x)g(-x)+"tan"(sinx)

    Text Solution

    |

  6. Identify the following functions: f(x)=cos["x"]+[(sinx)/2] where [dot...

    Text Solution

    |

  7. Identify the given functions whether odd or even or neither: f(x)={(x|...

    Text Solution

    |

  8. Let the function f(x)=x^2+x+sin x-cosx+log(1+|x|) be defined on the in...

    Text Solution

    |

  9. Which of the following function/functions is/are periodic? sgn(e^(-x))...

    Text Solution

    |

  10. Match the column

    Text Solution

    |

  11. Explain the term 'Mode'

    Text Solution

    |

  12. Find the fundamental period of f(x)=cosxcos2xcos3xdot

    Text Solution

    |

  13. Let f(x)={1+|x|,x<-1 [x],xgeq-1 , where [.] denotes the greatest integ...

    Text Solution

    |

  14. If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^2)]=2f(x)dot

    Text Solution

    |

  15. f(x) = (alpha x)/(x + 1) (x ne -1), then for what value of alpha , f{f...

    Text Solution

    |

  16. If the domain of y=f(x)i s[-3,2], then find the domain of g(x)=f(|[x]|...

    Text Solution

    |

  17. Let f be a function defined on [0,2]. The prove that the domain of fun...

    Text Solution

    |

  18. A function f has domain [-1,2] and range [0,1] . Find the domain and r...

    Text Solution

    |

  19. Let f(x)=tanx a n d g(f(x))=f(x-pi/4), where f(x)a n dg(x) are real ...

    Text Solution

    |

  20. Let g(x)=1+x-[x] and f(x)={-1,x < 0, 0, x=0 1, x > 0. Then for a...

    Text Solution

    |