$$g(t)=f(2t-3)$$

$$g\left( t \right) = f\left( {{t \over 2} - 3} \right)$$

$$g\left( t \right) = f\left( {2t - {3 \over 2}} \right)$$

$$g\left( t \right) = f\left( {{t \over 2} - {3 \over 2}} \right)$$

$${1 \over s}\left[ {{e^{ - 3s}} - {e^{ - 5s}}} \right]$$

$${1 \over s}\left[ {{e^{ - 5s}} - {e^{ - 3s}}} \right]$$

$${{{e^{ - 3s}}} \over s}\left[ {1 - {e^{ - 2s}}} \right]$$

$${1 \over s}\left[ {{e^{ - 5s}} - {e^{ - 3s}}} \right]$$