Find left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis when lower f left-parenthesis x right-parenthesis equals Start Fraction 2 over x plus 3 End Fraction and lower g left-parenthesis x right-parenthesis equals Start Fraction 1 over 2x End Fraction.

left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 4 x over 1 plus 6 x End Fraction
Image with alt text: left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 4 x over 1 plus 6 x End Fraction

left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 1 over x squared plus 3 x End Fraction
Image with alt text: left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 1 over x squared plus 3 x End Fraction

left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction x plus 3 over 4 End Fraction
Image with alt text: left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction x plus 3 over 4 End Fraction

left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 1 over x plus 3 End Fraction

Image with alt text: left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 1 over x plus 3 End Fraction