Range of f(x) = x^2 + 34x - 71 x^2 + 2x - 7 is - Vidyadip

MCQ

Range of $f(x) = \frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}}$ is

A
$[5, 9]$
✓
$( - \infty ,\;5] \cup [9,\;\infty )$
C
$(5, 9)$
D
None of these

✓

Answer

Correct option: B.

$( - \infty ,\;5] \cup [9,\;\infty )$

b
(b) Let $\frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}} = y$

$ \Rightarrow \,\,{x^2}(1 - y) + 2\,(17 - y)\,x + (7y - 71) = 0$

For real value of $x,\,\,{B^2} - 4AC \ge 0$

$ \Rightarrow \,\,{y^2} - 14y + 45 \ge 0\,\, \Rightarrow y \ge 9,\,\,y \le 5$ .

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