What is the inverse of f(x)=(1/4 x+6)^3 ?

The inverse of f(x)=(1/4 x+6)^3 is 4\sqrt[3]{x}-24

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inverse of f(x)=(1/4 x+6)^3

inverse

f (x) = (\frac{1}{4} x + 6)^{3}

Solution steps

y = (\frac{1}{4} x + 6)^{3}

Replace

x

with

y

x = (\frac{1}{4} y + 6)^{3}

Solve for

y, x = (\frac{1}{4} y + 6)^{3}

f (x) = \frac{9 - x}{x + 4}

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

f (x) = x^{2} + 3, x \leq 0

f (x) = \frac{x ^{2} + 6 x - 16}{x ^{2} - 4}

x^{2} - 4 x + 8

What is the inverse of f(x)=(1/4 x+6)^3 ?
The inverse of f(x)=(1/4 x+6)^3 is 4\sqrt[3]{x}-24