1rBTX 04. FUNCIONS/1.4.3 Composta i recíproca 1.4.3.13Q ComposicióAleatPolinRac Amb les funcions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«/mrow»«/mstyle»«/math»,
quina és funció composta (fog)(x) ?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>,</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>x</mi><mo>+</mo><mi>a</mi></mrow></mfrac><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>,</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>,</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>h</mi><mo>≠</mo><mi>i</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mn>1</mn><mi>x</mi></mfrac></mrow><mrow><mi>fc</mi><mo>=</mo><mfrac><mn>1</mn><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></mfrac></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mrow><mi>fc</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mrow><mi>fc</mi><mo>=</mo><mfrac><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>-</mo><mi>a</mi></mrow><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>+</mo><mi>a</mi></mrow></mfrac></mrow></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>15</mn></mtd></mtr></mtable></mfenced><mo>-</mo><mn>5</mn></mrow><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>15</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>20</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>10</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula f(«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=811838bc5450d417da81d477f7a8036d&cw=16&ch=10&cb=9" width="16" height="10" style="vertical-align: -1px;"/>)

Per aplicar f, cal pensar que la variable de f no és x, és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=811838bc5450d417da81d477f7a8036d&cw=16&ch=10&cb=9" width="16" height="10" style="vertical-align: -1px;"/>

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»fc«/mi»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=d27e29eb2e880623ad8f8bf8d19cdce9&cw=77&ch=13&cb=10" width="77" height="13" style="vertical-align: -3px;"/>

]]>