Home
Class 12
MATHS
A mapping f:RtoR which is defined as f(x...

A mapping `f:RtoR` which is defined as `f(x)=cosx,x""inR` is

A

One-one olny

B

Onto only

C

One-one onto

D

Neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
D
Let `x_(1),x_(2)inR`
Then, `f(x_(1))=f(x_(2))`
`impliescosx_(1)=cosx_(2)`
`impliesx_(1)2npipmx_(2)`
So, `x_(1)nex_(2)`
Hence, cos x is not one-one function. Now, let `y=cosx` We know, `-1lecosxle1`
`:.yin[-1,1]`
`[-1,1]subR`. So, cos x is into function, not onto. Hence, f(x)=cosx is neither one-one nor onto.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

Mapping f : R to R which is defined as f (x) = cos x,x in R will be

If f:RtoR is defined by f(x)=|x| , then

The function f(x)=e^(x),x""inR is

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 the f:RtoR be defined by f(x)=2x+cosx . Then f:

Let f:RtoR be a function defined as f(x)=x|x|, for each x""inR,R being the set of real numbers. Which one of the following is correct?

A function f:RrarrR is defined by f(x)=4x^(3)+5,x inR . Examine if f is one-one and onto.