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Question

The range of f(x)=12x26x+7 is
  1. (,0)[25,)
  2. (,0][25,)
  3. (0,25]
  4. [0,25]


Solution

The correct option is C (0,25]
f(x)=12x26x+7
2x26x+7>0,   xR(D=3656=20<0)
Now, let y=f(x)
y=12x26x+7(2y)x2(6y)x+7y1=0
for quadratic polynomial y0
Now, for xR
D036y24(2y)(7y1)05y22y0y[0,25]
But y0
Range is (0,25]

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