What is the inverse of f(x)=\sqrt[3]{((x^5))/2-7} ?

The inverse of f(x)=\sqrt[3]{((x^5))/2-7} is \sqrt[5]{2x^3+14}

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inverse of f(x)=\sqrt[3]{((x^5))/2-7}

inverse

f (x) = 3 \frac{( x ^{5} )}{2} - 7

5 2 x^{3} + 14

Solution steps

y = 3 \frac{x ^{5}}{2} - 7

Replace

x

with

y

x = 3 \frac{y ^{5}}{2} - 7

Solve for

y, x = 3 \frac{y ^{5}}{2} - 7

5 2 x^{3} + 14

\frac{1}{7}

f (x) = \frac{5 x + 9}{2 x - 7}

f (x) = \frac{( 2 x + 1 )}{3 x - 2}

\frac{x}{9 x - 1}

\frac{x ^{2}}{4}

What is the inverse of f(x)=\sqrt[3]{((x^5))/2-7} ?
The inverse of f(x)=\sqrt[3]{((x^5))/2-7} is \sqrt[5]{2x^3+14}