The given function is G(s) = e^(-4s)/(s+9).

The inverse Laplace transform of a function G(s) is given by L^-1{G(s)} = g(t).

The presence of the exponential term e^(-4s) in the function G(s) suggests a shift in the time domain. The shift theorem states that if G(s) = e^(-as)F(s), then its inverse Laplace transform is g(t) = u(t-a)L^-1{F(s)} where u(t-a) is the unit step function.

Here, a = 4 and F(s) = 1/(s+9).

The inverse Laplace transform of F(s) = 1/(s+9) is e^(-9t).

Therefore, the inverse Laplace transform of G(s) = e^(-4s)/(s+9) is g(t) = u(t-4)e^(-9(t-4)).

So, the inverse Laplace transform of the given function is g(t) = u(t-4)e^(-9(t-4)).

Question

The given function is G(s) = e^(-4s)/(s+9).

The inverse Laplace transform of a function G(s) is given by L^-1{G(s)} = g(t).

The presence of the exponential term e^(-4s) in the function G(s) suggests a shift in the time domain. The shift theorem states that if G(s) = e^(-as)F(s), then its inverse Laplace transform is g(t) = u(t-a)L^-1{F(s)} where u(t-a) is the unit step function.

Here, a = 4 and F(s) = 1/(s+9).

The inverse Laplace transform of F(s) = 1/(s+9) is e^(-9t).

Therefore, the inverse Laplace transform of G(s) = e^(-4s)/(s+9) is g(t) = u(t-4)e^(-9(t-4)).

So, the inverse Laplace transform of the given function is g(t) = u(t-4)e^(-9(t-4)).

Knowee AI · Accepted Answer

The given function is G(s) = e^(-4s)/(s+9).

The inverse Laplace transform of a function G(s) is given by L^-1{G(s)} = g(t).

The presence of the exponential term e^(-4s) in the function G(s) suggests a shift in the time domain. The shift theorem states that if G(s) = e^(-as)F(s), then its inverse Laplace transform is g(t) = u(t-a)L^-1{F(s)} where u(t-a) is the unit step function.

Here, a = 4 and F(s) = 1/(s+9).

The inverse Laplace transform of F(s) = 1/(s+9) is e^(-9t).

Therefore, the inverse Laplace transform of G(s) = e^(-4s)/(s+9) is g(t) = u(t-4)e^(-9(t-4)).

So, the inverse Laplace transform of the given function is g(t) = u(t-4)e^(-9(t-4)).

Determine the inverse Laplace transform ofG(s)=e−4ss+9𝐺(𝑠)=𝑒−4𝑠𝑠+9Note: You must use the notation u(t−c)𝑢(𝑡−𝑐) rather than uc(t)𝑢𝑐(𝑡) in order for your answer to be accepted by SOWISO.

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