Home
Class 12
MATHS
Consider a function f: [0, (pi)/(2)] to ...

Consider a function `f: [0, (pi)/(2)] to R` given by `f (x) = sin x and g : [0, (pi)/(2)] to R` given by `g (x) = cos x,` Show that f and g are one-one but f + g is not one-one.

Text Solution

Verified by Experts

The correct Answer is:
`f + g`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise EXERCISE 1.1|13 Videos

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise EXERCISE 1.2|11 Videos

  • PROBABILITY

    NCERT TELUGU|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

  • VECTOR ALGEBRA

    NCERT TELUGU|Exercise Miscellaneous Exercise on chapter 10|17 Videos

Similar Questions

Explore conceptually related problems

Prove that the function f: R to R, given by f (x) =2x, is one-one and onto.

Find gof and fog, if f: T to R and g : R to R are given by f (x) = cos x and g (x) = 3x ^(2). Show that gof ne fog.

Show that the function f: N to N, given by f (x) =2x, is one-one but not onto.

If f : R to R , g : R to R are defined by f (x) = 4x - 1 and g (x) = x ^(2) + 2 then find (gof) (x)

If f:R to R , g:R to R are defined by f(x) = 3x-1 and g(x) = x^(2) + 1 then find (fog)(2) .

If f : R to R , g : R to R are defined by f (x) = 4x - 1 and g (x) = x ^(2) + 2 then find go (fof) (0)

f:R rarr R , defined by f(x)=sinx and g:R rarrR , defined by g(x)=x^(2), (f_(o)g)(x)=

If f : R to R , g : R to R are defined by f (x) = 4x - 1 and g (x) = x ^(2) + 2 then find (fof) (x)

If f(x)=sin(sinx) an f f'(x) +tan xf'(x)+g(x)=0 , then g(x) is :

NCERT TELUGU-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Consider a function f: [0, (pi)/(2)] to R given by f (x) = sin x and g...

    Text Solution

    |

  2. Let f : R to R be defined as f (x) =10 x +7. Find the function g : R t...

    Text Solution

    |

  3. Let f:Wto W be defined as f (n)=n -1, if n is odd and f (n) =n +1, if ...

    Text Solution

    |

  4. If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

    Text Solution

    |

  5. Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f...

    Text Solution

    |

  6. Show that the function f: R to R given by f (x) = x ^(3) is injective...

    Text Solution

    |

  7. Give examples of two functions f:N to Z and g: Z to Z such that g o f ...

    Text Solution

    |

  8. Give examples of two functions f : N to N and g : N to N such g o f is...

    Text Solution

    |

  9. Given a non empty set X, consider P (X) which is the set of all subset...

    Text Solution

    |

  10. Find the number of all onto functins from the set {1,2,3..,n} to itsel...

    Text Solution

    |

  11. Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S...

    Text Solution

    |

  12. Consider the binary opertions **: R xx R to R and o : R xx R to R defi...

    Text Solution

    |

  13. Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as ...

    Text Solution

    |

  14. If A = {0,1,2,3,4,5} Define a binary operation * on A as a*b = {{:(a+b...

    Text Solution

    |

  15. Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defin...

    Text Solution

    |

  16. Let A = {1,2,3}. Then number of relations containing (1,2) and (1,3) w...

    Text Solution

    |

  17. Let A = {1,2,3}. Then number of equivalence relations containing (1,2)...

    Text Solution

    |

  18. Let f : R to R be the Signumb Function defined as f (x) = {{:(1",",...

    Text Solution

    |

  19. Number of binary opertions on the set {a,b} are

    Text Solution

    |