Question

If the Laplace transform of a function \(f(t)\) is given by \[ \frac{s+3}{(s+1)(s+2)}, \] then the value of \(f(\ln2)\) is

• A. \(0\)
• B. \(3\)
• C. \(2\)
• D. \(\dfrac34\)

Hint:

Remember these standard inverse Laplace transforms: \[ \boxed{ L^{-1}\left\{\frac1{s+a}\right\}=e^{-at} } \] After finding \(f(t)\), substitute the required value of \(t\) carefully using \[ e^{-\ln a}=\frac1a. \]

Answer 1

The Correct Option is D