Home
Class 12
MATHS
Let A={xinR:x" is not a positive integer...

Let `A={xinR:x" is not a positive integer "}`define a function `f:AtoR" such that "f(x)=(2x)/(x-1)`. Then f is

A

Injective but not surjective

B

Surjective but not injective

C

Neither injective nor surjective

D

Not injective

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)=(2x)/(x-1)," "f(x)=2+(2)/(x-1)`
`"Say "f(x(1))=f(x_(2))" "rArr" "2+(2)/(x_(1)-1)=2+(2)/(x_(2)-1)" "rArr" "x_(1)=x_(2)`
f is injective.
Since f is one-one. f will NOT be able to take values corresponding to the value of x when x would be an integer. Therefore, f can't have `RR` as its range.
Injective NOT surjective.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2) . Then f is

Let the function f be defined by f(x)=((2x+1)/(1-3x)) then f^(-1)(x) is

Let f: RtoR be function defined by f(x)=sin (2x-3) , then f is

Let R be the set of all real numbers and let f be a function from R to R such that f(X)+(X+1/2)f(l-X)=1, for all xinR." Then " 2f(0)+3f(1) is equal to-

Let f:R rarr R be a function defined as f(x)=(x^(2)-6)/(x^(2)+2) , then f is

Let a function f:(1, oo)rarr(0, oo) be defined by f(x)=|1-(1)/(x)| . Then f is

Let a function f:(0,infty)to[0,infty) be defined by f(x)=abs(1-1/x) . Then f is