Need help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

il63 [147K]3 years ago

5 0

Answer:

Step-by-step explanation:

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How to show these 2 problems are inverses

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$\bf \begin{cases}
f(x)=\sqrt[3]{7x-2}\\\\
g(x)=\cfrac{x^3+2}{7}
\end{cases}\\\\
-----------------------------\\\\
now
\\\\
f[\ g(x)\ ]\implies f\left[ \frac{x^3+2}{7} \right]\implies \sqrt[3]{7\left[ \frac{x^3+2}{7} \right]-2}\implies \sqrt[3]{x^3+2-2}
\\\\\\
\sqrt[3]{x^3}\implies x\\\\
-----------------------------\\\\
or
\\\\
g[\ f(x)\ ]\implies g\left[\sqrt[3]{7x-2}\right]\implies \cfrac{\left[\sqrt[3]{7x-2}\right]^3+2}{7}
\\\\\\
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thus f[ g(x) ] = x indeed, or g[ f(x) ] =x, thus they're indeed inverse of each other

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