How do you verify if $f(x)=x^5; g(x)root5x$ are inverse functions?

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Answer 1 · 2018-07-14T16:37:35

See below.

If $f(x)$ and $g(x)$ are inverses, then:

$f(g(x))=g(f(x))=x$

$(root(5)(x))^5=(root(5)(x^5))=x$

$x=x=x$

So $f(x)$ and $g(x)$ are inverses.

How do you verify if f(x)=x^5; g(x)root5xf(x)=x^5; g(x)root5x are inverse functions?