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Assertion (A) : y=2x+3 is a one to one r...

Assertion (A) : `y=2x+3` is a one to one real valued function.
Reason (R) : `x_(1)nex_(2)`
`impliesy_(1)ney_(2),y_(1)=2x_(1)+3,y_(2)=2x_(2)+3` for any two real `x_(1)andx_(2)`

A

Both A and R are individually true, and R is the correct explanation of A

B

Both A and R are individually true but R is not the correct explanation of A.

C

A is true but R is false.

D

A is false but R is true

Text Solution

Verified by Experts

The correct Answer is:
A
(A) Given function is
`y=2x+3`
Let `y_(1)=y_(2)("To show "x_(1)=x_(2))`
`implies2x_(1)+3=2x_(2)+3`
`implies2x_(1)=2x_(2)`
`impliesx_(1)=x_(2)`
Hence, `y=2x+3` is one-one real valued function.
(R) Since `y_(1)=y_(2)impliesx_(1)=x_(2)`
`:.x_(1)nex_(2)impliesy_(1)ney_(2)`
Thus, Both (A) and (R) are true and R is the correct explanation of A.
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