Question

if f^-1(x) is the inverse of f(x)=2e^-x, then f^-1(x)=

Answer 1

f(x) = 2e^-x
y = 2e^-x (rewrite f(x) as y
x = 2e^-y (interchange x and y)
ln(x) = ln(2e^-y) (take ln both sides to solve for y)
ln(x) = ln2 + ln(e^-y)
ln(x) = ln2 -y
y = ln2 - lnx
y = ln(2/x)
so f inverse is ln(2/x)