What is the inverse of f(x)=(4-10x)^{5/2} ?

The inverse of f(x)=(4-10x)^{5/2} is -(x^{2/5}-4)/(10)

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inverse of f(x)=(4-10x)^{5/2}

inverse

- \frac{x ^{\frac{2}{5}} - 4}{10}

Solution steps

y = (4 - 10 x)^{\frac{5}{2}}

Replace

x

with

y

x = (4 - 10 y)^{\frac{5}{2}}

Solve for

y, x = (4 - 10 y)^{\frac{5}{2}}

- \frac{x ^{\frac{2}{5}} - 4}{10}

What is the inverse of f(x)=(4-10x)^{5/2} ?
The inverse of f(x)=(4-10x)^{5/2} is -(x^{2/5}-4)/(10)