Question

Ignore the other language​

Answer 1

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

`f^(-1)`(x) = ln(3x - 1) ==> plug in
`f^(-1)`(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