CAT-2021-QA-Slot-1/Free CAT Question papers

4).

f(x) = <pre>uncaught exception: <b>Function get_magic_quotes_gpc() is deprecated (errno: 8192) in /var/www/html/pfindia/tinymce/js/tinymce/plugins/tiny_mce_wiris/integration/service.php at line #10Function get_magic_quotes_gpc() is deprecated</b><br /><br />in file: /var/www/html/pfindia/tinymce/js/tinymce/plugins/tiny_mce_wiris/integration/service.php line 10<br />#0 /var/www/html/pfindia/tinymce/js/tinymce/plugins/tiny_mce_wiris/integration/service.php(10): _hx_error_handler()
#1 {main}</pre> is negative if and only if

  1. -5 < x < -2 or 3 < x < 9

  2. -2 < x < 3 or x > 9

  3. x < -5 or 3 < x < 9

  4. x < -5 or -2 < x < 3


Explanation

By taking factors of numerator and denominator, the function can be written as

         f(x) = fraction numerator open parentheses x plus 5 close parentheses open parentheses X minus 3 close parentheses over denominator open parentheses x minus 9 close parentheses open parentheses x plus 2 close parentheses end fraction

         The function will be negative if and only if one or three of the factors are negative.

When x < -5, all factors are negative. If -5 < x < - 2, only (x +5) is positive. If  3 < x < 9, only (x – 9) is negative.

         Thus, f(x) = fraction numerator x squared plus 2 x minus 15 over denominator x squared minus 7 x minus 18 end fraction is negative if and only if  -5 < x < -2 or  3 < x < 9

Ans (1)

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