# 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 | 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)

`=-6-(16(x-3)^{1/3}+32)^{1/5}/2`

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.**