Well, we know that the tangent line will pass through (0,f(0)) and have slope of f'(0). Just write down y=ax+b and use these two conditions to obtain a,b.
(hint: a=f'(0) straight away)
For the tangent to the inverse function, it will pass through the point (f(0),0) and have a slope of 1/f'(0). Use the same argument here also.