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Let f(x)= [ 4^x+2^x+1 2^x-2^ x / 2 +1 ] and g(x)= [ 9 x^2+5 ] . Identify which of the following statement(s) is(are) correct? [Note: where [y] denotes greatest integer function less than or equal to y .]

Options

  1. ANumber of points of discontinuities of f(x) in (- , 0] is 2 .
  2. BNumber of points of discontinuities of g(x) in (- , ) is 2 .
  3. CNumber of points of discontinuities of f(x) g(x) in (- , ) is 7 .
  4. DNumber of points of discontinuities of f(x) g(x) in (- , ) is 6 .

Correct answer

C. Number of points of discontinuities of f(x) g(x) in (- , ) is 7 .

Step-by-step solution

f(x)= [2^x+2^ x / 2 +1 ] ; g(x)= [ 9 x^2+5 ] f(x) is discontinuous at 2 points in (- , 0] and g(x) is discontinuous at 2 points in (- , ]f(x) g(x)= [2^x+2^ x / 2 +1 ] [ 9 x^2+5 ]= [ array ll 0 & x (- ,-2) (2, ) -1 & x=-2 -2 & -3 & 7 & x=2 array .

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