Home
Class 11
MATHS
If f,g,\ h are three functions defined f...

If `f,g,\ h` are three functions defined from `R\ to\ R` as follows: Find the range of `f(x)=x^2`

Text Solution

Verified by Experts

As we know that square of a real number is always greater than 0
`⇒x^2≥0,f(x)≥0`
Range of first function =`[0,∞)`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos
  • GEOMETRIC PROGRESSIONS

    RD SHARMA|Exercise Solved Examples And Exercises|255 Videos

Similar Questions

Explore conceptually related problems

If f,g,\ h are three functions defined from R\ to\ R as follows: the range of h(x)=x^2+1

f, g and h are three functions defined from R to R as follows: (i) f(x)=x^(2) (ii) g(x)=x^(2)+1 (iii) h(x)=sinx Then, find the range of each function.

Consider f g and h are real-valued functions defined on R. Let f(x)-f(-x)=0 for all x in R, g(x) + g(-x)=0 for all x in R and h (x) + h(-x)=0 for all x in R. Also, f(1) = 0,f(4) = 2, f(3) = 6, g(1)=1, g(2)=4, g(3)=5, and h(1)=2, h(3)=5, h(6) = 3 The value of f(g(h(1)))+g(h(f(-3)))+h(f(g(-1))) is equal to

f and g are functions defined from R rarr R If f(x-2)=x^(2) and g(x)=(x+2)^(2) then f(x)+g(x-2)=?

Let f:R to R be the function defined by f(x) = (1)/(2-cos x), AA x in R. Then, find the range fo f .

Let y=f(x),y=g(x),y=h(x) be three invertible functions defined from R rarr R Then y=f(x)+g(x)+h(x) is

If f : [2,oo) to R be the function defined by f(x)=x^(2)-4x+5, then the range of f is

Classify the following functions f(x) defined in R to R as injective , surjective , both or none . f(x) = x^(2)

RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. Let f: R->R whre R^+ is the set of all positive real numbers, be such ...

    Text Solution

    |

  2. Write the following relations as sets of ordered pairs and find which ...

    Text Solution

    |

  3. If f,g,\ h are three functions defined from R\ to\ R as follows: Find ...

    Text Solution

    |

  4. If f,g,\ h are three functions defined from R\ to\ R as follows: the r...

    Text Solution

    |

  5. Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11 , 15 , 16}andf = {(1, 5), (2, 9...

    Text Solution

    |

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

    Text Solution

    |

  7. If A = {p,q,r, s} and B = {1, 2, 3}, find which of the following is n...

    Text Solution

    |

  8. If A = {p,q,r, s} and B = {1, 2, 3}, find which of the following is n...

    Text Solution

    |

  9. If A = {p,q,r, s} and B = {1, 2, 3}, find which of the following is n...

    Text Solution

    |

  10. If A = {p,q,r, s} and B = {1, 2, 3}, find which of the following is n...

    Text Solution

    |

  11. Let A = {9, 10 , 11 , 12 , 13}and let f : A ->Nbe defined by f(n) = th...

    Text Solution

    |

  12. The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10The rel...

    Text Solution

    |

  13. If f(x)=x^2, find (f(1. 1)-f(1))/((1. 1-1))

    Text Solution

    |

  14. If f(x)=3x^4-5x^2+9, find f(x-1) .

    Text Solution

    |

  15. If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , p...

    Text Solution

    |

  16. If f(x) = x^2 - 3x + 4, then find the values of x satisfying the equat...

    Text Solution

    |

  17. If f(x)=(x+1)/(x-1) , show that f{f(x)}=xdot

    Text Solution

    |

  18. If f(x)=\ {x^2,\ w h e n\ x<0 x ,\ w h e n\ 0lt=x<1 1/x ,\ w h e n\ ...

    Text Solution

    |

  19. If f(x)=(2x)/(1+x^2)\ , show that f(tantheta)=sin2theta)

    Text Solution

    |

  20. Find the domain of each of the following real valued function: f(x)=1/...

    Text Solution

    |