Given f(x)=2x+3 and g(x)=(x-3)/(2)

To find the composition of the functions $f(x)$ and $g(x)$, we need to substitute one function into the other.<br /><br />1. To find $f(g(x))$, we substitute $g(x)$ into $f(x)$:<br /> $f(g(x)) = f\left(\frac{x-3}{2}\right) = 2\left(\frac{x-3}{2}\right) + 3 = x - 3 + 3 = x$<br /><br />2. To find $g(f(x))$, we substitute $f(x)$ into $g(x)$:<br /> $g(f(x)) = g(2x+3) = \frac{(2x+3)-3}{2} = \frac{2x}{2} = x$<br /><br />Therefore, the composition of the functions $f(x)$ and $g(x)$ is:<br />$f(g(x)) = x$<br />$g(f(x)) = x$