Expression 10: "g" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals left parenthesis, "A" "x" plus "B" , right parenthesis natural log left parenthesis, "x" , right parenthesis plus "C" "x" plus StartFraction, "D" Over "x" , EndFraction plus "E" plus "F" natural log left parenthesis, ln left parenthesis, "x" plus 1 , right parenthesis plus 1 , right parenthesisg1x=Ax+Blnx+Cx+Dx+E+Flnlnx+1+1
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Expression 11: "g" Subscript, "a" 0 , Baseline left parenthesis, "x" , right parenthesis equals left brace, "x" greater than 0.5 : exp left parenthesis, "g" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis , StartFraction, pi Over sin left parenthesis, pi "x" , right parenthesis exp left parenthesis, "g" Subscript, 1 , Baseline left parenthesis, 1 minus "x" , right parenthesis , right parenthesis , EndFraction , right bracega0x=x>0.5:expg1x,πsinπxexpg11−x
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Expression 12: "s" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesis equals 3 "x" squared minus 2 "x" cubeds3x=3x2−2x3
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Expression 13: "s" Subscript, 5 , Baseline left parenthesis, "x" , right parenthesis equals 6 "x" to the 5th power minus 15 "x" to the 4th power plus 10 "x" cubeds5x=6x5−15x4+10x3
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Expression 14: "g" Subscript, "a" "s" , Baseline left parenthesis, "x" , right parenthesis equals exponent left parenthesis, "g" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis plus left parenthesis, ln left parenthesis, StartFraction, pi Over StartAbsoluteValue, sin left parenthesis, pi "x" , right parenthesis , EndAbsoluteValue , EndFraction , right parenthesis minus "g" Subscript, 1 , Baseline left parenthesis, 1 minus "x" , right parenthesis minus "g" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis "s" Subscript, 5 , Baseline left parenthesis, 1 minus min left parenthesis, "x" , 1 , right parenthesis , right parenthesis , right parenthesisgasx=expg1x+lnπsinπx−g11−x−g1xs51−minx,1
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Expression 15: "g" Subscript, "a" , Baseline left parenthesis, "x" , right parenthesis equals left brace, "x" greater than or equal to 1 : exp left parenthesis, "g" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis , "x" less than 0 : StartFraction, pi Over sin left parenthesis, pi "x" , right parenthesis exp left parenthesis, "g" Subscript, 1 , Baseline left parenthesis, 1 minus "x" , right parenthesis , right parenthesis , EndFraction , "g" Subscript, "a" "s" , Baseline left parenthesis, "x" , right parenthesis , right bracegax=x≥1:expg1x,x<0:πsinπxexpg11−x,gasx
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Expression 16: log left parenthesis, StartAbsoluteValue, StartFraction, "g" left parenthesis, "x" , right parenthesis Over "g" Subscript, "a" , Baseline left parenthesis, "x" , right parenthesis , EndFraction minus 1 , EndAbsoluteValue , right parenthesisloggxgax−1
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Expression 17: log left parenthesis, StartAbsoluteValue, StartFraction, "g" left parenthesis, 10 Superscript, "x" , Baseline , right parenthesis Over "g" Subscript, "a" , Baseline left parenthesis, 10 Superscript, "x" , Baseline , right parenthesis , EndFraction minus 1 , EndAbsoluteValue , right parenthesislogg10xga10x−1
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Expression 18: log left parenthesis, StartAbsoluteValue, StartFraction, "g" prime left parenthesis, "x" , right parenthesis Over "g" Subscript, "a" , Baseline prime left parenthesis, "x" , right parenthesis , EndFraction minus 1 , EndAbsoluteValue , right parenthesislogg′xga′x−1