AP EAMCET201923 Apr 2019Morning ShiftMathematicsFunctionsActual
Match the following ( array |c|c|c| & List I & List II (A) & array l f: R R is such that f(x)=p x+q (p 0), x R array & array l I. f is neither one-one nor onto array (B) & array l f: R R⁺ 0 is such that f(x)=x^2, x R array & array l II. f is both one-one and onto array (C) & array l f: N N is such that f(n)=n^2+2 n+3, n N array & array l III. f is one-one but not onto array (D) & array l f: R R is such that f(x)=2 (
Options
- A( array cc & A & B & C & D & II & IV & III & I array )
- B( array cc & A & B & C & D & II & IV & V & I array )
- C( array cc & A & B & C & D & II & I & III & V array )
- D( array cc & A & B & C & D & III & II & I & IV array )
Correct answer
A. ( array cc & A & B & C & D & II & IV & III & I array )
Step-by-step solution
(A) For function (f: R R ) is defined as (f(x)=p x+q,(p 0) ) is a linear function.] And linear functions are one-one and onto in set of real numbers ((R) ). So, ( A II ) (B) For function (f: R R⁺ 0 ) is defined as (f(x)=x^2 ) ( f(-1)=f(1)=1 ), so (f(x) ) is not one-one function but range of (f(x)=x^2 ) is ([0, ) ), ( x^2 0, x R . ) So, (f ) is onto but not one-one. So, ( B ) IV (C) For (f: N N ) is defined as (f(x)=n^2+2 n+3 ) is one-one but not onto because there is not value of (n ), for which (f(n)=3 ). So, ( C