Home
Class 12
MATHS
Let t the function f:RR to RR be defined...

Let t the function `f:RR to RR` be defined by, `f(x)=a^x(a gt0 ,a ne1).` Find
`{x:f(x) =1}`
Also show that, `f(x+y)=f(x).f(y) "for all "x,y in RR.`

Text Solution

Verified by Experts

The correct Answer is:
{0}
Promotional Banner

Topper's Solved these Questions

  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Short Answer Type Question|60 Videos

  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|72 Videos

  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Multiple choice question|28 Videos

  • REAL NUMBERS

    CHHAYA PUBLICATION|Exercise Exercise (Long Answer Type Questions)|10 Videos

  • RELATION AND FUNCTIONS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|3 Videos

Similar Questions

Explore conceptually related problems

Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). Find range of f

Let RR and RR^+ be the sets of real numbers and positive real numbers respectively. If f:RR^+ to RR be defined by f(x)=log_ex , find (a) range of f (b) {x:f(x)=1}. Also show that, f(xy)=f(x)+f(y).

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Let the function f:RR rarr RR and g:RR be defined by f(x) = sin x and g(x)=x^(2) . Show that, (g o f) ne (f o g) .

Let the function f:RR rarr RR be defined by , f(x)=4x-3 .Find the function g:RR rarr RR , such that (g o f) (x)=8x-1

Let the function f:RR rarr RR be defined by f(x)=x^(2) (RR being the set of real numbers), then f is __

Let the function f: RR rarr RR be defined by, f(x) =x^(2), . Find (i) f^(-1) (25) , (ii) f^(-1) (5) , (iii) f^(-1) (-5)

Let the functions f: RR rarr RR and g: RR rarr RR be defined by f(x)=x+1 and g(x)=x-1 Prove that , (g o f)=(f o g)=I_(RR)

Let, a in RR and let f:RR to RR be given by f(x)=x^(5)-5x-a . Then

CHHAYA PUBLICATION-RELATION AND MAPPING -Very short answer type questions
  1. Let A={-2,-1,0,1,3/2 ,2},B={-6,-5,-3,0,3,4} and f:AtoB be defined by f...

    Text Solution

    |

  2. Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). F...

    Text Solution

    |

  3. Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). F...

    Text Solution

    |

  4. Let A={0,1},B={2,6},andf:A to B be given by, f(x) =6-4x and g:A to B b...

    Text Solution

    |

  5. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  6. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  7. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  8. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  9. Find the image set of the domain of each of the following functions : ...

    Text Solution

    |

  10. Show that, f={(1,1),(-1,-5),(2,4),(3,7)} defines a mapping. If this ma...

    Text Solution

    |

  11. If the mapping {(1,2),(-1,6),(2,3),(3,6) is descibed by the rule f(x)=...

    Text Solution

    |

  12. Let f be subset of ZZxxZZ such that f={(xy,x-y):x,y inZZ} is f a mappi...

    Text Solution

    |

  13. If A={1,2,3,4,5}, show that the relation f={(x,y):x+y=6} for all x,y i...

    Text Solution

    |

  14. Let A = {1,2,3,4} and B = {7,8,9} , then which of the following relati...

    Text Solution

    |

  15. Let A = {1,2,3,4} and B = {7,8,9} , then which of the following relati...

    Text Solution

    |

  16. Let A = {1,2,3,4} and B = {7,8,9} , then which of the following relati...

    Text Solution

    |

  17. Let A = {1,2,3,4} and B = {7,8,9} , then which of the following relati...

    Text Solution

    |

  18. Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2, then f...

    Text Solution

    |

  19. Given y = 4 for all real values of x, Can y be regarded as a function ...

    Text Solution

    |

  20. The volume of an open tank with a square base of side x m is 40m^3. Ex...

    Text Solution

    |