Home
Class 12
MATHS
Suppose that f(x)f(f(x))=1 and f(1000)=9...

Suppose that `f(x)f(f(x))=1` and `f(1000)=999` then which of the following is true

A

`f(500)=(1)/(500)`

B

`f(199)=(1)/(199)`

C

`f(x)=(1)/(x)AA x in R-{0}`

D

`f(1999)=(1)/(1999)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`f(1000)f(f(1000))=1`
`rArr" "f(1000)f(999)=1`
`rArr" "999f(999)=1`
`therefore" "f(999)=(1)/(999)`
The numbers 999 and `(1)/(999)` are in the range of f.
Hence, by intermediate value property of continuous function, function takes all values between 999 and `(1)/(999)`, then there exists
`alpha in ((1)/(999),999)` such that `f(alpha)=500`
Then `f(alpha)f(f(alpha))=1 rArr f(500)=(1)/(500)`
Similarly, `199 in ((1)/(199),999),` thus `f(199)=(1)/(199)`
But there is nothing to show that 1999 lies in the range of f.
Thus (d) is not correct and (c) is alos incorrect.
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|7 Videos

  • FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE ENGLISH|Exercise DPP 3.4|14 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE ENGLISH|Exercise Exercises 1.18|1 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x(1-x)^(3) then which of following is true ?

Let f be a real valued function such that for any real x f(15+x)=f(15-x)and f(30+x)=-f(30-x) Then which of the following statements is true ?

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

Let f(x) be linear functions with the properties that f(1) le f(2), f(3) ge f(4) " and " f(5)=5. Which one of the following statements is true?

If f ''(x)|le 1 AA x in R, and f (0) =0=f' (0), then which of the following can not be true ?

Let f: R to R be a function defined by f(x)="min" {x+1,|x|+1}. Then, which of the following is true?

If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, then which of the following is true? (a) f(x+1)=f(x) (b) f(x+3)=f(x) (c) f(x+2)=f(x) (d) None of these

Let f: R->R be a function defined by f(x+1)=(f(x)-5)/(f(x)-3)AAx in R . Then which of the following statement(s) is/are true?

Let f'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) which of the following is true?

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?