What is the inverse of f(x)=(6-3x)^{5/2} ?

The inverse of f(x)=(6-3x)^{5/2} is -(x^{2/5}-6)/3

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inverse of f(x)=(6-3x)^{5/2}

inverse

f (x) = (6 - 3 x)^{\frac{5}{2}}

- \frac{x ^{\frac{2}{5}} - 6}{3}

Solution steps

y = (6 - 3 x)^{\frac{5}{2}}

Replace

x

with

y

x = (6 - 3 y)^{\frac{5}{2}}

Solve for

y, x = (6 - 3 y)^{\frac{5}{2}}

- \frac{x ^{\frac{2}{5}} - 6}{3}

What is the inverse of f(x)=(6-3x)^{5/2} ?
The inverse of f(x)=(6-3x)^{5/2} is -(x^{2/5}-6)/3