Home
Class 12
MATHS
If f(x) ={(x^(3)", " x lt1),(2x-1...

If ` f(x) ={(x^(3)", " x lt1),(2x-1", " x ge 1):} " and " g(x)={(3x", " x le2),(x^(2)", " x gt 2):} " then find " (f-g)(x).`

Text Solution

Verified by Experts

` f(x) ={(x^(3)", " x lt1),(2x-1", " 1 le x le 2),(2x-1", " x gt 2):} " and " g(x)={(3x", " x lt1),(3x", "1 le x le2),(x^(2)", " x gt 2):}`
` implies (f+g)(x) ={(x^(3)+3x", " x lt1),(2x-1+3x", " 1 le x le 2),(2x-1+x^(2)", " x gt 2):}`
`={(x^(3)+3x", " x lt1),(5x-1", " 1 le x le 2),(x^(2)+2x-1", " x gt 2):}`
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

f(x)={(log_(e)x",",0lt x lt 1),(x^(2)-1 ",",x ge 1):} and g(x)={(x+1",",x lt 2),(x^(2)-1 ",",x ge 2):} . Then find g(f(x)).

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} . Describe the function f//g and find its domain.

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",", x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} Then which of the following is/are true?

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If the domain of g(f(x))" is " [-1, 4], then

If f(x)={(2x^(2)+1",", x le1),(4x^(3)-1",",x gt 1):} , then int_(0)^(2)f(x)dx is

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} g(f(x)) is not defined if

The relation f is defined by f(x) ={(3x+2", "0le x le2),(x^(3)", "2 le x le 5):}. The relation g is defined by g(x) ={(3x+2", "0le x le1),(x^(3)", "1 le x le 5):} Show that f is a function and g is not a function

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is

Draw the graph of f(x) = {{:(x^(3)","x^(2) lt 1), (x","x^(2) ge 1):}

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. The relation f is defined by f(x) ={(3x+2", "0le x le2),(x^(3)", ...

    Text Solution

    |

  2. If f: [-3,4] to R,f(x)=2x, " and " g :[-2, 6] to R,g(x) =x^(2). Then f...

    Text Solution

    |

  3. If f(x) ={(x^(3)", " x lt1),(2x-1", " x ge 1):} " and " g(x)={(...

    Text Solution

    |

  4. Check the nature of the following function. (i) f(x)=sin x, x in R...

    Text Solution

    |

  5. Check the nature of the function f(x)=x^(3)+x+1, x in R using analyt...

    Text Solution

    |

  6. Let f: R->R \ w h e r e \ f(x)=(x^2+4x+7)/(x^2+x+1) . Is f(x) \ on e \...

    Text Solution

    |

  7. Let f:R to R where f(x) =sin x. Show that f is into. Also find the co...

    Text Solution

    |

  8. Let f: N->Z be a function defined as f(x)=x-1000. Show that f is an in...

    Text Solution

    |

  9. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

    Text Solution

    |

  10. Let A={x:-1 le x le 1}=B be a function f: A to B. Then find the nature...

    Text Solution

    |

  11. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  12. If f:[0,oo) to [0,1), " and " f(x)=(x)/(1+x) then check the nature o...

    Text Solution

    |

  13. If the functions f(x) and g(x) are defined on R -> R such that f(x)=...

    Text Solution

    |

  14. Show that f: R->R defined by f(x)=(x-1)(x-2)(x-3) is surjective but no...

    Text Solution

    |

  15. Let f : R to R be a function such that f(x)=x^3+x^2+3x+sinx . Then

    Text Solution

    |

  16. Let f : R to R be a function such that f(x)=x^3+x^2+3x+sinx . Then

    Text Solution

    |

  17. If function f(x) is defined from set A to B, such that n(A)=3 and n(B)...

    Text Solution

    |

  18. Find the range of f(x)=x^2-2x-4.

    Text Solution

    |

  19. Find the domain of the following f(x)=sqrt(x^(2)-5x+4) "

    Text Solution

    |

  20. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

    Text Solution

    |