What is the inverse of f(x)= 1/2 x^4 ?

The inverse of f(x)= 1/2 x^4 is \sqrt[4]{2}\sqrt[4]{x},-\sqrt[4]{2}\sqrt[4]{x}

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inverse of f(x)= 1/2 x^4

inverse

f (x) = \frac{1}{2} x^{4}

Solution steps

y = \frac{1}{2} x^{4}

Replace

x

with

y

x = \frac{1}{2} y^{4}

Solve for

y, x = \frac{1}{2} y^{4}

x^{4} - 9 x^{2}

f (x) = 9 x - 4

3 x

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

What is the inverse of f(x)= 1/2 x^4 ?
The inverse of f(x)= 1/2 x^4 is \sqrt[4]{2}\sqrt[4]{x},-\sqrt[4]{2}\sqrt[4]{x}