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Travis Fogle

Answered question

2021-11-30

Use function composition to determine if f (x) and g (x) are inverse functions.
$f (x) = \sqrt[3]{x + 1} a n d g (x) = x^{3} + 1$

Answer & Explanation

romancemrf

Beginner2021-12-01Added 14 answers

Viven functions
$f (x) = \sqrt[3]{x + 1}, g (x) = x^{3} + 1$
we know that,
using composition functions
If f(x) and g(x) are invevsc functions then.
$f (g (x)) = x, g (f (x)) = x$
Checking
$f (g (x)) = f (x^{3} + 1)$
$= \sqrt[3]{(x^{3} + 1) + 1}$
$f (g (x)) = \sqrt[3]{x + 2} \neq x$ .
$g (f (x)) = g (\sqrt[3]{x + 1})$
$= (\sqrt[3]{x + 1})^{3} + 1$
$= (x + 1) + 1$
$g (f (x)) = x + 2 \neq x$
$g (f (x)) = f (g (x)) \neq x$
So,they ave not invevsc functions

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