laplace inverse transformation
\$I(s)=\frac{s}{7s+6}\$

Multiply by \$\frac{1}{7}\frac{1}{\frac{1}{7}}\$

\$I(s)=\frac{1}{7}\frac{s}{s+\frac{6}{7}}\$

Move out s from the numerator so we got a 1 there so we can use the laplace transform of \$\frac{1}{s+a}\mathcal{L}e^{-at}\$

\$I(s)=s\frac{1}{7}\frac{1}{s+\frac{6}{7}}\$

So a factor s in laplace domain is a derivation in time domain, a factor \$\frac{1}{7}\$ is just a scaling, the last factor is the \$e^{-at}\$

The answer is the derivative of this expression: \$\frac{1}{7}e^{-\frac{6t}{7}}\$

I will let you do that step so I don't take all the glory. 



Here's a link if you need more help.