Answer:
x >= 1/3
Explanation:
y = (e^x + 1)/3
x = (e^y + 1)/3 ==> inverse function is when you switch x and y
3*x = 3 * (e^y + 1)/3 ==> solve for y by first multiplying both sides by 3
3x = e^y + 1
3x - 1 = e^y + 1 - 1
3x - 1 = e^y ==> now take natural log on each side to isolate y
ln(3x - 1) = ln(e^y)
y = ln(3x - 1) ==> simplify
(x) = ln(3x - 1) ==> plug in
(x) for y to indicate the inverse function
3x - 1 >= 0 ==> you can't have the log function of a negative number
3x - 1 + 1 >= 0 + 1 ==> add 1 on both sides to isolate x
3x >= 1
3x/3 >= 1/3
x >= 1/3