Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x^3 + 4 and g(x) = cube root(x - 4)

Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x^3 + 4 and g(x) = cube root(x - 4)

mathstudent55 · Answer

$f(x) = x^3 + 4 $

$g(x) =  \sqrt[3]{x - 4} $

$f(g(x)) = f(\sqrt[3]{x - 4}) $ 

$ ~~~~~~~~~~~~~= ( \sqrt[3]{x - 4})^3 + 4 $

$~~~~~~~~~~~~~= x - 4 + 4$

$~~~~~~~~~~~~~ = x$

Now try doing the same for $g(f(x))$.

anonymous · Answer

your job is to compute 
$$f(g(x))=f(\sqrt[3]{x-4})=(\sqrt[3]{x-4})^3+4$$ and see that you get $x$

anonymous · Answer

oh, what @mathstudent55  said!