Home
Class 9
MATHS
If the polynomial f(x) be defined by f...

If the polynomial f(x) be defined by
`f(x) = {{:(2x^(2)-3 " when " xle2),(2x+1 " when "2ltxle4),(1/(2x-1) "when "xgt4):}`
then find `(a)f(sqrt2),(b)f(pi)`.

Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.3|36 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.4|52 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.1|57 Videos

  • LOGARITHM

    CALCUTTA BOOK HOUSE|Exercise Exercise - 7 (Long-answer type questions)|49 Videos

  • PROBABILITY

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 2|16 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(2x^(2)+3" when " x le 2,),(2x+1 " when "2 lt x le 3,),((1)/(2x-1) " when "x gt 3,):} then f( e) =

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

Let f(x)=2x^2-3," when "x le2 =2x+1," when "2ltxle3 =(1)/(2x-1)," when "xgt3 Find f(0),f(3),f(-2),f(4),f(sqrt(2)) and f(e).

If the function f be defined by f(x) =(2x +1)/(1-3x) , then f ^(-1) (x) is-

f(x)={:{(x^2,"when "x lt0),(x,"when "0 lexlt1),(1/x,"when "x ge1):} Value of f(-sqrt3) is___

f(x)={:{(x^2,"when "x lt0),(x,"when "0 lexlt1),(1/x,"when "x ge1):} Value of f(1/2) is____

f(x)={:{(x^2,"when "x lt0),(x,"when "0 lexlt1),(1/x,"when "x ge1):} Value of f(sqrt3) is_____

The polynomial f(x) is defined by f(x)={{:("0 when x is an integer ,"),("1 when x is not an integer ,"):} Then compute : (a)f(-2),(b)f(sqrt3) .

If f, RR to RR is defined by f (x) ={{:((x-2)/(x ^(2) -3x+2)"," ,"when " x in RR-{1","2}),(2",","when" x=1),(1",", "when" x=2):} then lim _(xto2) (f(x) -f(2))/(x-2) is equal to-

A continuous function f(x) is defined as follows : f(x)={{:(x,"when "xlt1),(ax+bx^(2),"when "1lexle2),(2x^(2),"when "xgt2):} Find the values of a and b.

CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.2
  1. If f(x)=(1-x)/(1+x), then prove that f(x)+f(1/x)=0.

    Text Solution

    |

  2. Find the zeroes of the polynomial p(x)=x^(2)-(a+1/a)x+1.

    Text Solution

    |

  3. If f(x)=log(2)xandg(x)=x^(2) then find f(g(2)).

    Text Solution

    |

  4. If f(x)=x^(2)andg(x)=sqrtx, then prove that g(f(4)) = 4.

    Text Solution

    |

  5. If f(x)=4^(x), then prove that (f(x+1))/(f(x-1))=16.

    Text Solution

    |

  6. The polynomial f(x) is defined by f(x)={{:("0 when x is an integer ,...

    Text Solution

    |

  7. If the polynomial f(x) be defined by f(x) = {{:(2x^(2)-3 " when " xl...

    Text Solution

    |

  8. If f(x) = ax + b, f(0) = 2 and f(4) = 10, then find the values of a an...

    Text Solution

    |

  9. If 2f(x) + 3f(-x) = 15 - 4x, then prove that f(x) = 3 + 4x.

    Text Solution

    |

  10. If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the va...

    Text Solution

    |

  11. If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values...

    Text Solution

    |

  12. If f(x)=1/(4x^(2)), then proved that (f(x-h)-f(x+h))/h=x/((x^(2)-h^(2)...

    Text Solution

    |

  13. If y=f(x)=(2x+3)/(5x-a), then determine the value of a so that x = f(y...

    Text Solution

    |

  14. If f(x) = (x-1)/(x+1), then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/...

    Text Solution

    |

  15. If 2f(x-1)-f((1-x)/x)=x, then prove that 3f(x)=2(x+1)+1/(x+1).

    Text Solution

    |

  16. If xgt0, then prove that the value of the polynomial (2x+2^(-x)-2) is ...

    Text Solution

    |

  17. If f(x)=(x-a)/x+x/(x-b), then find f((a+b)/2).

    Text Solution

    |

  18. If 3f(x)-f(1/x)=log(e)x^(4)(xgt0), then prove that f(e^(x))=x.

    Text Solution

    |

  19. If f(x)=x^(9)-2x^(8)-2x^(6)+4x^(5)+x^(4)-2x^(3)+x-1, then find the val...

    Text Solution

    |

  20. If f(x)=(a-x^(n))^(1/n),agt0 and n is a positive integer, then prove t...

    Text Solution

    |