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$The range of the function f (x) = \frac{e^{x} - e^{| x |}}{e^{x} + e^{| x |}} is$

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(−∞,∞)

[0,1)

(−1,0]

(−1,1)

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detailed solution

Correct option is C

f(x)=ex−e|x|ex+e|x|=0, x≥0ex−e−xex+e−x, x<0 Clearly, f(x) is identically zero if x≥0----(1)∵ x<0 e2x<1 or 00 and 1+y1−y<1 or (y+1)(y−1)<0 and 2y1−y<0 i.e., −11 or −1

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The range of the function f(x)=ex−e|x|ex+e|x| is

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$The range of the function f (x) = \frac{e^{x} - e^{| x |}}{e^{x} + e^{| x |}} is$