Q99 / 160 · AP EAMCET 2023 (15 May Shift 2) · Mathematics

The function $f(x)=\sqrt{\frac{3 x^2-5 x-2}{2 x^2-7 x+5}}$ has discontinuous points at $\mathrm{x}=$

  • A
    $5 / 2,2$
  • B
    $-1 / 3,2$
  • Correct answer
    C
    $1,5 / 2$
  • D
    $-1 / 3,1$

Solution

Given the function $f(x)=\sqrt{\frac{3 x^2-5 x-2}{2 x^2-7 x+5}}$ $=\sqrt{\frac{3 x^2-5 x-2}{2 x^2-2 x-5 x+5}}=\sqrt{\frac{3 x^2-5 x-2}{(2 x-5)(x-1)}}$ So given function is discontinuous at $x=1, \frac{5}{2}$

Hence, the correct answer is option: 'C'.

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