SOLUTION: Hi, Given f(x)=2x^3-7, find f^-1(x)

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Question 903481: Hi,
Given f(x)=2x^3-7, find f^-1(x)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
When you have f%5E-1 it means that the question is asking you to find the inverse. This means that the original function f%28x%29=2x%5E3-7 is reflected along the line y=x+.

so, what you do is change all the x values to y values and all the y values to x values(f%28x%29 is also known as y)

if y=2x%5E3-7 then f%28x%29%5E-1 is:

x=2y%5E3-7
solve for y+
x%2B7=2y%5E3
%28x%2B7%29%2F2=y%5E3
+root%283%2C%28x%2B7%29%2F2%29+=y

so f%28x%29%5E%28-1%29+=+root%283%2C%28x%2B7%29%2F2%29+ or f%28x%29%5E%28-1%29+=+root%283%2C%28x%2B7%29%29%2Froot%283%2C2%29%29