What is the inverse of f(x)=5ln(sqrt(1+8x^3)) ?

The inverse of f(x)=5ln(sqrt(1+8x^3)) is (\sqrt[3]{e^{(2x)/5}-1})/(2)

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inverse of f(x)=5ln(sqrt(1+8x^3))

inverse

f (x) = 5 ln (1 + 8 x^{3})

\frac{3 e ^{\frac{2 x}{5}} - 1}{2}

Solution steps

y = 5 ln (1 + 8 x^{3})

Replace

x

with

y

x = 5 ln (1 + 8 y^{3})

Solve for

y, x = 5 ln (1 + 8 y^{3})

\frac{3 e ^{\frac{2 x}{5}} - 1}{2}

f (x) = \frac{5}{6} x - 1

3 - 3 - 1

3 - \frac{2}{x}

\frac{D}{D x} 4 x + 10 x^{2}

f (x) = 2 x^{\frac{5}{2}} + 4

What is the inverse of f(x)=5ln(sqrt(1+8x^3)) ?
The inverse of f(x)=5ln(sqrt(1+8x^3)) is (\sqrt[3]{e^{(2x)/5}-1})/(2)