Home
Class 12
MATHS
Let g(x)=1+x-[x] "and ...

Let g(x)=1+x-[x]
`"and " f(x)={{:(-1","x lt 0),(0","x=0),(1","x gt 0):}`
Then, for all x, find f(g(x)).

Text Solution

Verified by Experts

The correct Answer is:
f(g(x))=1
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|6 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is

Let f(x) = {:{(|x| for 0<|x|le1), (1 for x = 0):} then

Let f be a continuous function satisfying f '(l n x)=[1 for 0 1 and f (0) = 0 then f(x) can be defined as (a) f(x)={(1 , "if"x le 0 ),(1-e^(x), "if" x gt 0 ):} " " (b) f(x)={(1,"if" x le 0 ),(e^(x)-1,"if" x gt 0):} (c) f(x)={(x,"if" x lt 0),(e^(x),"if" x gt 0 ):} " " (d) f(x)={(x,"if" x le 0 ),(e^(x)-1,"if" x gt 0):}

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

Examine the function, f(x) = {{:(x - 1",",x lt 0),(1//4",",x = 0),(x^(2)-1",",x gt 0):} Discuss the continuity and if discontinuous remove the discontinuity.

Let f(x) = sin x and " g(x)" = {{:(max {f(t)","0 le x le pi},"for", 0 le x le pi),((1-cos x)/(2)",","for",x gt pi):} Then, g(x) is

Let f : R to R be the signum function defined as f(x) = {{:(1, x gt 0),(0, x =0),(-1, x lt 0):} and g: R to R be the greatest integer function given by g(x) = [x] where [x] is greatest integer less than or equal to x. Then, does fog and gof coincide in (0,1] ?

f(x)={{:(x-1",", -1 le xle 0),(x^(2)",",0 lt x le 1):} and g(x)=sinx. Find h(x)=f(abs(g(x)))+abs(f(g(x))).

Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x le 0),(x-1",",1 lt x le 2):} and g(x)=f(|x|) +|f(x)| . Then find g(x) .

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let g(x)=1+x-[x] "and " f(x)={{:(-1","x l...

    Text Solution

    |

  2. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

    Text Solution

    |

  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

    Text Solution

    |

  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  5. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  6. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

    Text Solution

    |

  7. Let f(x)=x^2a n dg(x)=sinx for all x in R Then the set of all x satis...

    Text Solution

    |

  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

    Text Solution

    |

  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g(f(x)) is invertible in the do...

    Text Solution

    |

  13. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (a) (...

    Text Solution

    |

  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

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

    Text Solution

    |

  17. Let E={1,2,3,4} and F={1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  18. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  19. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  20. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

    Text Solution

    |

  21. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

    Text Solution

    |