Home
Class 12
MATHS
about to only mathematics...

about to only mathematics

Text Solution

Verified by Experts

y = f(x) and y = g(x) are mirror image of each other about y = a.
` (##CEN_GRA_C01_S01_012_S01.png" width="80%">
For some `x = b, g(b) - a - f(b)`
` rArr f(b) + g(b) = 2a`
` rArr h(b) = f(b) + g(b) = 2a` (constant)
Hence h (x) is a constant function. Thus, it is neither one-one, nor onto.
Promotional Banner

Topper's Solved these Questions

  • GETTING STARTED WITH GRAPHS

    CENGAGE|Exercise Exercise|18 Videos

  • FUNCTIONS

    CENGAGE|Exercise Question Bank|21 Videos

  • GRAPH OF INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|18 Videos

Similar Questions

Explore conceptually related problems

A school library has 75 books on Mathematics, 35 books on physics. A student can choose only one book , In how many ways a student can choose a book on Mathematics or physics?

The first theorem in mathematics is ………… .

There are 15 candidates for an examination . 7 candidates are appearing for mathematics examination while the remaining 8 are appearing for different subjects. In how many ways can they be seated in a row so that no two mathematics candidates are together ?

There are 15 candidates for an examination. 7 candidates are appearing for mathematics examination while the remaning 8 are appearing for different subjects. In how many ways can they be seated in a row so that no two mathematics candidates are together?

There are 15 candidates for an examination. 7 candidates are appearing for mathematics examination while the remaining 8 are appearing for different subjects . In how many ways can they be seated in a row so that no two mathematics candidates are together ?

A bag contains a total of 20 books on physics and mathematics, Any possible combination of books is equally likely. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 3 books on mathematics.

The probability that a student will score centum in mathematics is (4)/(5) . The probability that he will not score centum is ............

CENGAGE-GETTING STARTED WITH GRAPHS-Exercise
  1. about to only mathematics

    Text Solution

    |

  2. Does the following graph pass the vertical or horizontal line test ?

    Text Solution

    |

  3. Consider the graph of y = f(x) as shown in the following figure. ...

    Text Solution

    |

  4. Which of the following functions has (have) y-symmetry or origin symme...

    Text Solution

    |

  5. The graph of functions are given in the following fingure. Discuss the...

    Text Solution

    |

  6. Check weather the following function/functions is/are periodic or not?...

    Text Solution

    |

  7. Suppose that f is even, periodic function with period 2, and that f(x)...

    Text Solution

    |

  8. The graph of y = f(x) is as shown in the following figure. Find t...

    Text Solution

    |

  9. The graph of f is shown. State, with reason, the numbers at which f is...

    Text Solution

    |

  10. If f:R→R, g:R→R are given by f(x)=(x+1)^2 and g(x)=x^2+1 , then w...

    Text Solution

    |

  11. (a) Can the graph of the function intersect the horizontal asymptote? ...

    Text Solution

    |

  12. The graph of y = f(x) is given with six labelled points. Anser the fol...

    Text Solution

    |

  13. Graph of functions are given in the following figure. Check the funct...

    Text Solution

    |

  14. In the following graph, state the absolute and local maximum and mini...

    Text Solution

    |

  15. Prove : ((1+cot^2 A)/(1+tan^2 A​))=((1−cotA)/(1−tanA​))^2=tan^2 A

    Text Solution

    |

  16. Evaluate int(0)^(pi/2)(sinx/(cosx+sinx))dx

    Text Solution

    |

  17. The figure shows the graphs of f, f' and f''. Indentify each curve and...

    Text Solution

    |

  18. Match the graph of y = f(x) in Column I with the corresponding graph ...

    Text Solution

    |

  19. If f(x) is an even function, then f'(x). If in a △ABC, atan A+ btan B=...

    Text Solution

    |