What is the inverse of f(x)=(6x^3+7)^{1/5} ?

The inverse of f(x)=(6x^3+7)^{1/5} is cube root of (x^5-7)/6

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inverse of f(x)=(6x^3+7)^{1/5}

inverse

f (x) = (6 x^{3} + 7)^{\frac{1}{5}}

Solution steps

y = (6 x^{3} + 7)^{\frac{1}{5}}

Replace

x

with

y

x = (6 y^{3} + 7)^{\frac{1}{5}}

Solve for

y, x = (6 y^{3} + 7)^{\frac{1}{5}}

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

f (x) = x - 5 + 6

f (x) = x - 5 + 7

f (x) = 3 (\frac{1}{2} x - 7)^{2} + 8

2

What is the inverse of f(x)=(6x^3+7)^{1/5} ?
The inverse of f(x)=(6x^3+7)^{1/5} is cube root of (x^5-7)/6