Home
Class 12
MATHS
If f: R->R is a function satisfying the ...

If `f: R->R` is a function satisfying the property `f(2x+3)+f(2x+7)=2AAx in R ,` then find the fundamental period of `f(x)`.

Text Solution

Verified by Experts

The correct Answer is:
8
`f(2x+3)+f(2x+7)=2 " (1)" `
Replacing x by `x+2,f(2x+7)+f(2x+11)=2 " (2)" `
From (1) -(2), we get
`f(2x+3)-f(2x+11)=0`
or `f(2x+3)=f(2x+11)`
Replace `2x+3` by x. Then
`f(x)=f(x+8)`
Hence, fundamental period of `y=f(x)` is 8`.
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

If f:R->R is a function satisfying the property f(x+1)+f(x+3) = 2 for all x in R than fi s (1) periodic with period 3. (2) periodic with period 4. (3) non periodic. (4) periodic with period 5.

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

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

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

If f: R->R is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

Let a function f:R to R be defined by f(x)=2x+cosx+sinx " for " x in R . Then find the nature of f(x) .

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

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Determine all functions f : R rarr R satisfying f(x-f(y)) = f(f(y)) + ...

    Text Solution

    |

  2. Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdo...

    Text Solution

    |

  3. If f: R->R is a function satisfying the property f(2x+3)+f(2x+7)=2AAx ...

    Text Solution

    |

  4. If f(x) is an even function and satisfies the relation x^2dotf(x)-2f(1...

    Text Solution

    |

  5. If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a g...

    Text Solution

    |

  6. A real-valued function f(x) satisfies the functional equation f(x-y)=...

    Text Solution

    |

  7. Draw the graph of y=sin|x|.

    Text Solution

    |

  8. Draw the graph of the function: |f(x)|=tanx

    Text Solution

    |

  9. Draw the graph of the function: f(x)=|x^2-3|x|+2|

    Text Solution

    |

  10. Draw the graph of the function: f(x)=-|x-1|^(1/2)

    Text Solution

    |

  11. Find the total number of solutions of sinpix=|in|x||

    Text Solution

    |

  12. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

    Text Solution

    |

  13. Draw the graph and find the points of discontinuity for f(x)=[x^(2)-x-...

    Text Solution

    |

  14. The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)} on a set A={1, 2,...

    Text Solution

    |

  15. Let P={(x,y)|x^(2)+y^(2)=1,x,yinR}. Then, P, is

    Text Solution

    |

  16. Let R be an equivalence relation on a finite set A having n elements....

    Text Solution

    |

  17. A relation R on the set of complex number is defined by z1 R z2 iff (z...

    Text Solution

    |

  18. Which one of the following relations on R is an equivalence relation?

    Text Solution

    |

  19. Let R be the relation on the set R of all real numbers defined by aRb ...

    Text Solution

    |

  20. The function f: NvecN(N is the set of natural numbers) defined by f(n)...

    Text Solution

    |