Home
Class 12
MATHS
Let f:R to R be a function satisfying f...

Let `f:R to R ` be a function satisfying `f(2-x)=f(2+x) and f(20-x)=f(x) AA x in R.` For this function `f`, answer the following.
The graph of `y= f(x)` is not symmetrial about
(a) symmetrical about `x=2` (b) symmetrical about `x=10` (c) symmetrical about `x=8` (d) None of these

A

symmetrical about `x=2`

B

symmetrical about `x=10`

C

symmetrical about `x=8`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(2-x) =f(2+x) " (1)" `
Replace x by `2-x. " Then " f(x)=f(4-x) " (2)" `
Also, given `f(20-x)=f(x) " (3)" `
From (1) and (2), `f(4-x)=f(20-x).`
Replace x by `4-x. " Then " f(x)=f(x+16).`
Hence, the period of `f(x)` is 16.
`f(2-x)=f(2+x)`
Hence, `y=f(x)` is symmetrical about `x=2`.
Also, `f(20-x)=f(x)`
`or f(20-(10+x))=f(10+x)`
`or f(10-x)=f(10+x)`
Hence, `y=f(x)` is symmetrical about `x=10`.
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) AA x in R. For this function f , answer the following. If f(2) ne f(6), then the

A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R then f is

If the graph of the function f(x) is symmetrical about x = 20 then

Let f : R to R be a function such that f(x)=x^3+x^2+3x+sinx . Then

Let f be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x^3phi(x) for all x and y when phi (x) is a continuous function then f''(x) is equal to

f(x) is real valued function, satisfying f(x+y)+f(x-y)=2f(X),f(y) for all y ne R , then

If f(x) is a real-valued function defined as f(x)=In (1-sinx), then the graph of f(x) is (A) symmetric about the line x =pi (B) symmetric about the y-axis (C) symmetric and the line x=(pi)/(2) (D) symmetric about the origin

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let R rarr R be a function such that f(x+y) = f(x)+f(y) AA x, y in R . If f(x) is differentiable at x= 0, then

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",...

    Text Solution

    |

  2. Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) ...

    Text Solution

    |

  3. Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) ...

    Text Solution

    |

  4. Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) ...

    Text Solution

    |

  5. Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x...

    Text Solution

    |

  6. Find the domain and range of h(x) = g(f(x), where f(x) = {([x], -2l...

    Text Solution

    |

  7. Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x...

    Text Solution

    |

  8. Consider a function f whose domain is [-3, 4] and range is [-2, 2] wit...

    Text Solution

    |

  9. Consider a function f whose domain is [-3, 4] and range is [-2, 2] wit...

    Text Solution

    |

  10. Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f...

    Text Solution

    |

  11. Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f...

    Text Solution

    |

  12. Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f...

    Text Solution

    |

  13. The function f(x) is defined on the interval [0.1] Then match the foll...

    Text Solution

    |

  14. Match the following lists:

    Text Solution

    |

  15. Let f(x)=(x^(2)-6x+5)/(x^(2)-5x+6). Then match the expressions/statem...

    Text Solution

    |

  16. Match the following lists:

    Text Solution

    |

  17. Match the following lists:

    Text Solution

    |

  18. Match the following lists:

    Text Solution

    |

  19. { . } denotes the fractional part function and [.] denotes the greates...

    Text Solution

    |

  20. Let f be a real-valued invertible function such that f((2x-3)/(x-2))=5...

    Text Solution

    |