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Ignore the other language​

Ignore the other language​-example-1

1 Answer

3 votes

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


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

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