If f(x) = $\{\begin{array}{cc}\hfill x+a,x\le 0\hfill & \hfill \left|x-4\right|,x>0\hfill \end{array}andg(x)=\{\begin{array}{cc}\hfill x+1,x<0\hfill & \hfill {\left(x-4\right)}^2+b,x\ge 0\hfill \end{array}$ are continuous on R, then (gof)(2) + (fog)(-2) is equal to:

<p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>f</mi> <mrow> <mo> (</mo> <mrow> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo> {</mo> <mrow> <mtable> <mtr columnalign="center"> <mtd columnalign="center"> <mi>x</mi> <mo>+</mo> <mi>a</mi> <mo>, </mo> </mtd> <mtd columnalign="center"> <mi>x</mi> <mo>? </mo> <mn>0</mn> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <mrow> <mo>|</mo> <mrow> <mi>x</mi> <mo>? </mo> <mn>4</mn> </mrow> <mo>|</mo> </mrow> <mo>, </mo> </mtd> <mtd columnalign="center"> <mi>x</mi> <mo>&gt;</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> </mrow> <mtext>? </mtext> <mtext>? </mtext> <mtext>? </mtext> <mtext>? </mtext> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mtext>? </mtext> <mtext>? </mtext> <mtext>? </mtext> <mi>g</mi> <mrow> <mo> (</mo> <mrow> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo> {</mo> <mrow> <mtable> <mtr columnalign="center"> <mtd columnalign="center"> <mi>x</mi> <mo>+</mo> <mn>1</mn> <mo>, </mo> </mtd> <mtd columnalign="center"> <mi>x</mi> <mo>&lt;</mo> <mn>0</mn> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mi>x</mi> <mo>? </mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mo>, </mo> </mtd> <mtd columnalign="center"> <mi>x</mi> <mo>? </mo> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> </mrow> </mrow> </math> </span></p><p><span lang="EN-IN"><span class="mathml" contenteditable="false"> <math> <mrow> <mo>? </mo> </mrow> </math> </span> &nbsp; &nbsp;</span><span lang="EN-IN">f (x) and g (x) are continuous on R <span class="mathml" contenteditable="false"> <math> <mrow> <mo>? </mo> </mrow> </math> </span></span><span lang="EN-IN">&nbsp;a = 4 and b = 1 – 16 = 15</span></p><p><span lang="EN-IN">then (gof) (2) + (fog) (</span><span lang="EN-IN">-</span><span lang="EN-IN">2) = g (2) + f (-1) = -11 + 3 = -8</span></p><p><span lang="EN-IN">&nbsp;</span></p>

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