$\bf \begin{cases}
f(x)=\sqrt[3]{7x-2}\\\\
g(x)=\cfrac{x^3+2}{7}
\end{cases}\\\\
-----------------------------\\\\
now
\\\\
f[\ g(x)\ ]\implies f\left[ \frac{x^3+2}{7} \right]\implies \sqrt[3]{7\left[ \frac{x^3+2}{7} \right]-2}\implies \sqrt[3]{x^3+2-2}
\\\\\\
\sqrt[3]{x^3}\implies x\\\\
-----------------------------\\\\
or
\\\\
g[\ f(x)\ ]\implies g\left[\sqrt[3]{7x-2}\right]\implies \cfrac{\left[\sqrt[3]{7x-2}\right]^3+2}{7}
\\\\\\
\cfrac{7x-2+2}{7}\implies \cfrac{7x}{7}\implies x$

thus f[ g(x) ] = x indeed, or g[ f(x) ] =x, thus they're indeed inverse of each other

8 0

3 years ago

Michael has $12,500 to invest. he invests part in an account which earns 4.2% annual interest and the rest in an account which e

Dimas [21]

Suppose he invest x dollars in one account, y in the other
x+y=12,500
0.042x+0.062y=669.50
multiple the first equation by 0.042: 0.042x+0.042y=525
subtract this new equation from equation 2: 0.02y=144.50
y=7225
x=12500-7225=5275

8 0

3 years ago

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