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.

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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