JEE Main202524 Jan 2025Evening ShiftMathematicsFunctionsActual

The function f:(- , ) (- , 1) , defined by f(x)= 2^x-2^ -x 2^x+2^ -x is :

Options

ANeither one-one nor onto
BOnto but not one-one
CBoth one-one and onto
DOne-one but not onto

Correct answer

D. One-one but not onto

Step-by-step solution

aligned & f ( x )= 2^ 2 x -1 2^ 2 x +1 & =1- 2 2^ 2 x +1 & f ^ ( x )= 2 (2^ 2 x +1 )^2 2.2^ 2 x 2 i.e always + ve aligned so f(x) is function aligned & f (- )=-1 & f ( )=1 & f ( x ) (-1,1) co-domain aligned so function is one-one but not onto

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