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AP EAMCET202017 Sep 2020Evening ShiftMathematicsFunctionsActual

The function (f(x)= sech (x) ) on ( R ) has the range

Options

  1. A((0, ) )
  2. B((0,1] )
  3. C([1, ) )
  4. D((1, ) )

Correct answer

B. ((0,1] )

Step-by-step solution

(f(x)= sech x ) (= 1 x = 2 e^x+e^ -x ) At ( x=0, f(x)= 2 e^0+e⁻⁰ = 2 2 =1 ) At (x 0, f(x) ) is less than 1 or (e^x+e^ -x ) is greater than 2 . Also (f(x) 0 ) at any value of (x ). Hence, range ( sech x ) (=(0,1] )

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