Why does "Solve" not work for integral?

Question

I have defined the following function:

f1[c_] := -Integrate[E^(-t), {t, 0, y}] - 
   Integrate[E^((-c)*t), {t, y, -Log[1/2]}]

When I solve this for c=1, I get f1(1)=-0.5.

However,

Solve[f1[y] == -0.5, y]

returns no solution. What am I doing wrong?

Thanks in advance!

Answer 1

This works, using Reals

Solve[f1[y] == -1/2, y, Reals]//N

ps. better to use exact numbers with Solve. so 1/2 instead of 0.5.

see help on Solve