given f(x)=8x^5, find f^-1(x) Then state whether f^1(x) is a function.
Mathematics · High School · Mon Jan 18 2021
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Given the numerical equation:
f(x) = 8x^5
Determine the inverse of the function.
Solution:
In order to determine the inverse of the function, we simply equate f(x) as y, then interchange the position of x and y, and lastly solve for y.
f(x) = 8x^5
y = 8x^5
x = 8y^5
Divide both sides by 8 in order to cancel out 8y^5
8y^5/8 = x/5
y^5 = x/5
Take the 5th root of both sides in order to cancel out y^5, hence we can also designate the 5th root by raising both sides with 1/5
(y^5)^1/5 = (x/5)^1/5
y = (x/5)^1/5
Final answer:
y = (x/5)^1/5