State if the given functions are inverses. `g(x)=(x-3)^{1/3}+2`  `f(x)=-6-(16x)^{1/5}/2` 

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lfryerda eNotes educator| Certified Educator

Two functions `f(x)` and `g(x)` are inverses provided `f(g(x))=x` .  This means to check if the functions are inverses, then we need to check the composition to find x.

`f(g(x))=-6-(16g(x))^{1/5}/2`   sub in g(x)


We can easily see that this does not equal x.  This is verified by substituting x=1 into the composition and not getting 1 as a result.

The two functions are not inverses.