What is the inverse of f(x)=(x^{1/2}+7)^3 ?

The inverse of f(x)=(x^{1/2}+7)^3 is x^{2/3}-14\sqrt[3]{x}+49

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inverse of f(x)=(x^{1/2}+7)^3

inverse

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

Solution steps

y = (x^{\frac{1}{2}} + 7)^{3}

Replace

x

with

y

x = (y^{\frac{1}{2}} + 7)^{3}

Solve for

y, x = (y^{\frac{1}{2}} + 7)^{3}

\frac{x - 4}{x - 2}

f (x) = 2 x^{2} + x - 14

- 2 x^{2} + 6 x

y = - \frac{1}{3} x + 2

f (x) = - 6 x

What is the inverse of f(x)=(x^{1/2}+7)^3 ?
The inverse of f(x)=(x^{1/2}+7)^3 is x^{2/3}-14\sqrt[3]{x}+49