SOLUTION: 1. Given two functions, f(x) and g(x), explain how to determine algebraically if f and g are inverses of each other. 2. Let (x)=5x^3+2, and g(x)=(x-3/5)^1/3. Determine algebraica

Algebra ->  Functions -> SOLUTION: 1. Given two functions, f(x) and g(x), explain how to determine algebraically if f and g are inverses of each other. 2. Let (x)=5x^3+2, and g(x)=(x-3/5)^1/3. Determine algebraica      Log On


   

Question 684486: 1. Given two functions, f(x) and g(x), explain how to determine algebraically if f and g are inverses of
each other.
2. Let (x)=5x^3+2, and g(x)=(x-3/5)^1/3. Determine algebraically if f and g are inverses of each other.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
f%5E-1%28x%29 solve for x
...
y = 5x%5E3%2B2
y+-+2+=+5x%5E3
%28y-2%29%2F5+=+x%5E3
root%283%2C%28y-2%29%2F5%29+=+root%283%2Cx%5E3%29
x = root%283%2C%28y-2%29%2F5%29+=+%28%28y-2%29%2F5%29%5E%281%2F3%29
...
f%5E-1%28x%29+=+%28%28x-2%29%2F5%29%5E%281%2F3%29
...
no g(x) is not an inverse, unless you mistyped x-3 instead of x-2
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