Home
Class 12
MATHS
Find the range of the following (i) f...

Find the range of the following
(i) `f(x)="sgn"(x^(2)) " (ii) "f(x)="sgn"(x^(2)-2x+3)`

Text Solution

Verified by Experts

(i) We know that `x^(2) ge 0 AA x in R`
` :. "sgn"(x^(2))={(0",",x^(2)=0),(1",",x^(2) ne 0):}={(0",",x=0),(1",",x ne 0):}`
Hence range of f(x) is `{0,1}`
(ii) ` x^(2)-2x+3=(x-1)^(2)+2gt 0 AA x in R.`
So, `f(x)= "sgn" (x^(2)-2x+3)=1`
Hence, range of f(x) is `{1}`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.1|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.2|5 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the domain and range of the following (i) f(x)=sqrt(x^(2)-3x+2) " (ii) " f(x)=sqrt(x^(2)-4x+6)

Find the range of the following (i) f(x) = x^(2) (ii) f(x) = x (iii) f(x) = x^(2) + 2 (iv) f(x) = x^(3)

Write the equivalent definition and draw the graphs of the following functions. (a) f(x)=sgn(log_(e)|x|) (b) f(x)=sgn(x^(3)-x)

Find the domain and range of the following functions. (i) f(x)=sqrt(2x-3) " (ii) " f(x) =(1)/(x-2) (iii) f(x) =x^(2) +3 " (iv) " f(x)=(1)/(x^(2)+2)

Which of the following is true for f(x)=sgn(x)xx sin x

Find the domain and range of the following real functions: ( )f(x)=-|x|( ii) f(x)=sqrt(9-x^(2))

Sketch the graphs of the following functions: f(x)=sgn(ln x)

Find the range of f(x)=sgn(x^(2)-2x+3)

For the following functions write the piecewise definition and draw the graph (i) f(x)=" sgn "(log_(e)x) " (ii) "f(x) = " sgn "(sin x)

f(x)=x sgn (x^(2)) should be

CENGAGE-RELATIONS AND FUNCTIONS-Solved Examples And Exercises
  1. Find the range of the following (i) f(x)="sgn"(x^(2)) " (ii) "f...

    Text Solution

    |

  2. Find the inverse of the function: f:(-oo,1] rarr [1/2,oo],w h e r ef(...

    Text Solution

    |

  3. Find the value of x for which function are identical. f(x)=xa n dg(x)=...

    Text Solution

    |

  4. Find the value of x for which function are identical. f(x)=cosxa n dg(...

    Text Solution

    |

  5. Find the value of x for which function are identical. f(x)=(sqrt(9-x^2...

    Text Solution

    |

  6. Find the inverse of the function: f: R rarr (-oo,1)gi v e nb yf(x)=1-...

    Text Solution

    |

  7. f:(2,3)vec(0,1)d efin e db yf(x)=x-[x],w h e r e[dot] represents the g...

    Text Solution

    |

  8. Find the inverse of the function: f(x)={x^3-1, ,x<2x^2+3,xgeq2

    Text Solution

    |

  9. Find the inverse of the function: f:[-1,1]rarr[-1,1]defined byf(x)=x|...

    Text Solution

    |

  10. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

    Text Solution

    |

  11. Let f(x)=(9^x)/(9^x+3) . Show f(x)+f(1-x)=1 and, hence, evaluate. f(1/...

    Text Solution

    |

  12. If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

    Text Solution

    |

  13. Let g(x) be a function such that g(a+b)=g(a)dotg(b)AAa , b in Rdot If...

    Text Solution

    |

  14. Find the value of x for which function are identical. f(x)=tan^(-1)x+t...

    Text Solution

    |

  15. The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in ...

    Text Solution

    |

  16. Plot y=|x|,y=|x-2|, and y=|x+2|

    Text Solution

    |

  17. If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...

    Text Solution

    |

  18. If for all real values of ua n dv ,2f(u)cosv=(u+v)+f(u-v), prove that ...

    Text Solution

    |

  19. If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= ...

    Text Solution

    |

  20. If f: X rarr[1,oo) is a function defined as f(x)=1+3x^3, find the su...

    Text Solution

    |

  21. Find the period (if periodic) of the following function ([.] denotes ...

    Text Solution

    |