Range of the function y -2 x -2- x -2 x -2- x isA- RB- -1-1C- -1-1-D- 0-1

The correct option is B ( 1,1) 2^x+2^ x is always gt;0 i.e., domain is R y = 2^x 2^ x/2^x + 2^ x=2^2x 1/2^2x+1 ⇒ 1+y/1 y=2.2^2x/2 (componendo divid ...

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Standard XII

Mathematics

Definition of Function

Range of the ...

Question

$R a n g e o f t h e f u n c t i o n y = \frac{2^{x} - 2^{- x}}{2^{x} + 2^{- x}} i s$

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Solution

The correct option is B
(-1,1)

$2^{x} + 2^{- x} i s a l w a y s > 0 i . e ., d o m a i n i s R y = \frac{2^{x} - 2^{- x}}{2^{x} + 2^{- x}} = \frac{2^{2 x} - 1}{2^{2 x} + 1} \Rightarrow \frac{1 + y}{1 - y} = \frac{{2.2}^{2 x}}{2} (c o m p o n e n d o d i v i d e n d o) = 2^{2 x} > 0 \Rightarrow \frac{1 + y}{1 - y} > 0 i . e \frac{(1 + y)^{2}}{1 - y^{2}} > 0 \Rightarrow 1 - Y^{2} > 0 \Rightarrow - 1 < y < 1$

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Range of the function y=2x−2−x2x+2−x is

The correct option is B (-1,1) 2x+2−x is always >0 i.e., domain is Ry=2x−2−x2x+2−x=22x−122x+1⇒ 1+y1−y=2.22x2 (componendo dividendo)=22x>0⇒ 1+y1−y>0 i.e (1+y)21−y2>0⇒ 1−Y2>0 ⇒ −1<y<1

$R a n g e o f t h e f u n c t i o n y = \frac{2^{x} - 2^{- x}}{2^{x} + 2^{- x}} i s$