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.
If `f(2) ne f(6),` then the

A

(a) fundamental period of `f(x) " is " 1`

B

(b) fundamental period of `f(x) " may be " 1`

C

(c) period of `f(x)` cannot be 1

D

(d) fundamental period of `f(x) " is " 8`

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.
If 1 is a period, then `f(x)=f(x+1) AA x in R`
`or f(2)=f(3)=f(4)=f(5)=f(6)`
which contradicts the given hypotheses that `f(2) ne f(6).`
Therefore, 1 cannot be period of `f(x)`.
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. 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 function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R then f is

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

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x ,AAx in Rdot Then find the value of f(0)dot

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

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

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

Let f : RtoR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3),x in R . Then f(2) equals

Let f :R R- {3/5}rarrR-{2/5} be a function defined as f (x)= (2x)/(5x+3 .Find the inverse of the function f.

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) ...

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

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

    Text Solution

    |

  13. Match the following lists:

    Text Solution

    |

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

    Text Solution

    |

  15. Match the following lists:

    Text Solution

    |

  16. Match the following lists:

    Text Solution

    |

  17. Match the following lists:

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Let f(x)=3x^2-7x+c , where c is a variable coefficient and x >7/6 . Th...

    Text Solution

    |