Express the function f in terms of the unit step function an

Express the function f in terms of the unit step function and its translations. Then find L(f). f (x) = {4x, 0 lessthanorequalto x

Solution

f(x) = 4x( u(x) - u(x - 4) ) + 3( u(x - 4) ) , where u(x) denotes the step function

Taking Laplace Transform

L[ f(x) ](s) = (4/s²) - (4e^-4s/s²) - (13e^-4s/s)