SOLUTION: Given f(x)=x^3+2 and g(x)=cube_root(x-2), show that f(g(x))=x and g(f(x))=x. Graph both functions on the same set of coordinate axes.

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Question 113796: Given f(x)=x^3+2 and g(x)=cube_root(x-2), show that f(g(x))=x and g(f(x))=x. Graph both functions on the same set of coordinate axes.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
#3

Start with f(x)

Plug in


Replace each with . This is given since


Cube the cube root (these two functions "undo" each other and cancel out)


Combine like terms


So this shows that


Start with g(x)


Plug in


Replace f(x) with


Combine like terms


Take the cube root of to get x. Remember the cube root and the cube cancel each other out.




So this shows that


Now if we graph the two functions, we get



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