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

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detailed solution

Correct option is C

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

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The range of the function, fx=ex-exex+ex

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