AP EAMCET Engineering 2018 Apr 22 Shift 2 Paper

If a and <fmath alttext=" b\ ( a> b )  " class="fm-inline"><mrow><mrow><mi class="fm-mi-length-1" mathvariant="italic">b</mi><mi class="fm-mi-length-1 ma-upright" mathvariant="normal" style="padding-right: 0px;"> </mi></mrow><mrow><mo class="fm-mo-Luc">(</mo><mrow><mi class="fm-mi-length-1" mathvariant="italic">a</mi><mo class="fm-infix-loose">></mo><mi class="fm-mi-length-1" mathvariant="italic">b</mi></mrow><mo class="fm-mo-Luc">)</mo></mrow></mrow></fmath> are points of discontinuity of the function  <br><div class="hscrollenable"><fmath alttext="f(x)=\{\table 3-2x,{,}\for,x≤0;2x+3,{,}\for,0<x≤1;2x^2-3x,{,}\for,1<x<2;2x-3,{,}\for, 2≤x<3;{|x|},{,}\for,x≥3" class="fm-inline"><mrow><mrow><mi class="fm-mi-length-1" mathvariant="italic" style="padding-right: 0.44ex;">f</mi><mrow><mo class="fm-mo-Luc">(</mo><mi class="fm-mi-length-1" mathvariant="italic">x</mi><mo class="fm-mo-Luc">)</mo></mrow></mrow><mo class="fm-infix-loose">=</mo><mrow class="ma-repel-adj"><mo class="fm-mo-Luc" style="font-size: 7.293em; vertical-align: -0.216em; display: inline-block; transform: scaleX(0.5);">{</mo><span class="fm-vert" mtagname="mtable"><table><tbody><tr class="fm-mtr" mtagname="mtr"><td class="fm-mtd" mtagname="mtd"><mrow><mn>3</mn><mo class="fm-infix">−</mo><mrow><mn>2</mn><mi class="fm-mi-length-1" mathvariant="italic">x</mi></mrow></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow class="ma-repel-adj"><mo>,</mo><mspace width=".17em" style="margin-right: 0.17em; padding-right: 0.001em; visibility: hidden;">‌</mspace><mi mathvariant="normal" class="ma-repel-adj">for</mi></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow><mi class="fm-mi-length-1" mathvariant="italic">x</mi><mo class="fm-infix-loose">≤</mo><mn>0</mn></mrow></td></tr><tr class="fm-mtr" mtagname="mtr"><td class="fm-mtd" mtagname="mtd"><mrow><mrow><mn>2</mn><mi class="fm-mi-length-1" mathvariant="italic">x</mi></mrow><mo class="fm-infix">+</mo><mn>3</mn></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow class="ma-repel-adj"><mo>,</mo><mspace width=".17em" style="margin-right: 0.17em; padding-right: 0.001em; visibility: hidden;">‌</mspace><mi mathvariant="normal" class="ma-repel-adj">for</mi></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow><mrow><mn>0</mn><mo class="fm-infix-loose"><</mo><mi class="fm-mi-length-1" mathvariant="italic">x</mi></mrow><mo class="fm-infix-loose">≤</mo><mn>1</mn></mrow></td></tr><tr class="fm-mtr" mtagname="mtr"><td class="fm-mtd" mtagname="mtd"><mrow><mrow><mn>2</mn><msup><mi class="fm-mi-length-1" mathvariant="italic">x</mi><span class="fm-script fm-inline" style="vertical-align: 0.7em;"><mn>2</mn></span></msup></mrow><mo class="fm-infix">−</mo><mrow><mn>3</mn><mi class="fm-mi-length-1" mathvariant="italic">x</mi></mrow></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow class="ma-repel-adj"><mo>,</mo><mspace width=".17em" style="margin-right: 0.17em; padding-right: 0.001em; visibility: hidden;">‌</mspace><mi mathvariant="normal" class="ma-repel-adj">for</mi></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow><mrow><mn>1</mn><mo class="fm-infix-loose"><</mo><mi class="fm-mi-length-1" mathvariant="italic">x</mi></mrow><mo class="fm-infix-loose"><</mo><mn>2</mn></mrow></td></tr><tr class="fm-mtr" mtagname="mtr"><td class="fm-mtd" mtagname="mtd"><mrow><mrow><mn>2</mn><mi class="fm-mi-length-1" mathvariant="italic">x</mi></mrow><mo class="fm-infix">−</mo><mn>3</mn></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow class="ma-repel-adj"><mo>,</mo><mspace width=".17em" style="margin-right: 0.17em; padding-right: 0.001em; visibility: hidden;">‌</mspace><mi mathvariant="normal" class="ma-repel-adj">for</mi></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow><mn>2</mn><mo class="fm-infix-loose">≤</mo><mrow><mi class="fm-mi-length-1" mathvariant="italic">x</mi><mo class="fm-infix-loose"><</mo><mn>3</mn></mrow></mrow></td></tr><tr class="fm-mtr" mtagname="mtr"><td class="fm-mtd" mtagname="mtd"><mrow><mo class="fm-mo-Luc">|</mo><mi class="fm-mi-length-1" mathvariant="italic">x</mi><mo class="fm-mo-Luc">|</mo></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow class="ma-repel-adj"><mo>,</mo><mspace width=".17em" style="margin-right: 0.17em; padding-right: 0.001em; visibility: hidden;">‌</mspace><mi mathvariant="normal" class="ma-repel-adj">for</mi></mrow></td><td class="fm-mtd" mtagname="mtd"><mrow><mi class="fm-mi-length-1" mathvariant="italic">x</mi><mo class="fm-infix-loose">≥</mo><mn>3</mn></mrow></td></tr></tbody></table></span></mrow></mrow></fmath></div> then <fmath alttext="3a -b   =" class="fm-inline"><mrow><mrow><mrow><mn>3</mn><mi class="fm-mi-length-1" mathvariant="italic">a</mi></mrow><mo class="fm-infix">−</mo><mi class="fm-mi-length-1" mathvariant="italic">b</mi></mrow><mo class="fm-infix-loose">=</mo></mrow></fmath>