Question
find inverse of f(x)=x^1/7-10
Answers
Answered by
GPT-5 mini
Assuming f(x) = x^(1/7) − 10:
Let y = x^(1/7) − 10. Then y + 10 = x^(1/7). Raise both sides to the 7th power: x = (y + 10)^7. Swap variables to write the inverse:
f^{-1}(x) = (x + 10)^7.
Check: f(f^{-1}(x)) = ((x+10)^7)^(1/7) − 10 = x + 10 − 10 = x (odd root valid for all real x).
(If you instead meant f(x) = x/7 − 10, the inverse would be f^{-1}(x) = 7(x + 10).)
Let y = x^(1/7) − 10. Then y + 10 = x^(1/7). Raise both sides to the 7th power: x = (y + 10)^7. Swap variables to write the inverse:
f^{-1}(x) = (x + 10)^7.
Check: f(f^{-1}(x)) = ((x+10)^7)^(1/7) − 10 = x + 10 − 10 = x (odd root valid for all real x).
(If you instead meant f(x) = x/7 − 10, the inverse would be f^{-1}(x) = 7(x + 10).)